Enter any three inputs to calculate the other two values
How to use this Free Fall Calculator 🤔
There are input fields for Initial velocity \((u)\), Time of fall \((t)\), Acceleration due to gravity \((g)\), Final velocity \((v)\), and Height \((h)\). Enter any three inputs to calculate the other two values.
The calculator uses the \( v = u + g \cdot t \) \( h = u \cdot t + \frac{1}{2} g \cdot t^2 \) formula, substitues given values, and calcuates the missing value.
The missing value is calcuated and displayed in the input field. Also, the caculation is displayed under the input section.
What is Free Fall?
Free fall refers to the motion of an object falling under the influence of gravity alone, without any air resistance. The key parameters in free fall are time of fall (t), final velocity (v), height (h), initial velocity (u), and the acceleration due to gravity (g).
Calculating Final Velocity and Height
The final velocity of an object in free fall is calculated using the formula:
\( v = u + g \cdot t \).
The height from which the object falls is calculated using the formula:
\( h = u \cdot t + \frac{1}{2} g \cdot t^2 \).
Input and Output Combinations of the Free Fall Calculator
Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.
Calculator InputsSet #1
t Time of fall
u Initial velocity
g Acceleration due to gravity
For these given inputs,
Outputs, Formulas
We calculate the following outputs:
Final velocity\(v = \)\( u + g \cdot t \)
Height\(h = \)\( u \cdot t + \frac{1}{2} g \cdot t ^2 \)
Initial velocity\(u = \)\( \frac{ h - \frac{1}{2} g \cdot t ^2 }{ t } \)
Final velocity\(v = \)\( \frac{ h + \frac{1}{2} g \cdot t^2 }{ t } \)
Calculator InputsSet #6
h Height
v Final velocity
g Acceleration due to gravity
For these given inputs,
Outputs, Formulas
We calculate the following outputs:
Time of fall\(t = \)\( \frac{ v + \sqrt{ v ^2 - 2 g h } }{ g } \)
Initial velocity\(u = \)\( v - g \cdot t \)
Calculator InputsSet #7
t Time of fall
u Initial velocity
h Height
For these given inputs,
Outputs, Formulas
We calculate the following outputs:
Acceleration due to gravity\(g = \)\( \frac{ 2 \cdot ( h - u \cdot t ) }{ t ^2 } \)
Final velocity\(v = \)\( u + g \cdot t \)
Examples
1
Consider that a person dropped an object from the top of a building with an initial velocity of 4 m/s. The object travelled for 10 s before touching the ground. What is the final velocity of object, and height of the building?
Answer
Given:
Time of fall, t = 10 s
Initial velocity, u = 4 m/s
Acceleration due to gravity, g = 9.81 m/s²
Calculating final velocity (v)...
\( v = \) \( u + g \cdot t \)
\( v = \) \(4+9.81\times10\)
\( v = \) 102.1 m/s
Calculating height (h)...
\( h = \) \( u \cdot t + \frac{1}{2} g \cdot t ^2 \)
\( h = \) \(4\times10+ \frac{1}{2} \times9.81\times10^2 \)
\( h = \) 530.5 m
2
Consider that a person dropped an object from the top of a building with an initial velocity of 0 m/s. The object travelled for 2 s before touching the ground. What is the final velocity of object, and height of the building?
Answer
Given:
Time of fall, t = 2 s
Initial velocity, u = 0 m/s
Acceleration due to gravity, g = 9.81 m/s²
Calculating final velocity (v)...
\( v = \) \( u + g \cdot t \)
\( v = \) \(0+9.81\times2\)
\( v = \) 19.62 m/s
Calculating height (h)...
\( h = \) \( u \cdot t + \frac{1}{2} g \cdot t ^2 \)
\( h = \) \(0\times2+ \frac{1}{2} \times9.81\times2^2 \)
\( h = \) 19.62 m
3
Consider that a bird dropped a toy from top of an electric pole. The initial velocity of the toy is 4 m/s. The toy reached a final velocity of 20 m/s before touching the ground. What is the height of the pole, and time taken by the toy to reach the ground?
Answer
Given:
Final velocity, v = 20 m/s
Initial velocity, u = 4 m/s
Acceleration due to gravity, g = 9.81 m/s²
Calculating time of fall (t)...
\( t = \) \( \frac{ v - u }{ g } \)
\( t = \) \( \frac{20-4}{9.81} \)
\( t = \) 1.631 s
Calculating height (h)...
\( h = \) \( u \cdot \frac{ v - u }{ g } + \frac{1}{2} g \cdot \left( \frac{ v - u }{ g } \right)^2 \)
Consider that a bird dropped chicken lollipop from top of a building of height 50 m. Since, the bird slipped it, consider that initial velocity is 0 m/s. Calculate the time taken by the chicken lollipop to reach ground, and also its final velocity with which it makes contact with ground.
Answer
Given:
Height, h = 50 m
Initial velocity, u = 0 m/s
Acceleration due to gravity, g = 9.81 m/s²
Calculating time of fall (t)...
\( t = \) \( \frac{ - u + \sqrt{ u ^2 + 2 g h } }{ g } \)
The same bird throwed another chicken lollipop from top of another building. Consider that we somehow calculated the final velocity to be 50 m/s, time to reach the ground to be 5 s. Calculate the initial velocity of the chicken lollipop with which the bird has thrown it, and also height of the building.
Answer
Given:
Final velocity, v = 50 m/s
Time of fall, t = 5 s
Acceleration due to gravity, g = 9.81 m/s²
Calculating initial velocity (u)...
\( u = \) \( v - g \cdot t \)
\( u = \) \(50-9.81\times5\)
\( u = \) 0.95 m/s
Calculating height (h)...
\( h = \) \(( v - g \cdot t ) \cdot t + \frac{1}{2} g \cdot t ^2 \)
\( h = \) \((50-9.81\times5) \times5+ \frac{1}{2} \times9.81\times5^2 \)
\( h = \) 127.375 m
Input and Output Combinations of the Free Fall Calculator
Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.
Calculator InputsSet #1
t Time of fall
u Initial velocity
g Acceleration due to gravity
For these given inputs,
Outputs, Formulas
We calculate the following outputs:
Final velocity\(v = \)\( u + g \cdot t \)
Height\(h = \)\( u \cdot t + \frac{1}{2} g \cdot t ^2 \)
Initial velocity\(u = \)\( \frac{ h - \frac{1}{2} g \cdot t ^2 }{ t } \)
Final velocity\(v = \)\( \frac{ h + \frac{1}{2} g \cdot t^2 }{ t } \)
Calculator InputsSet #6
h Height
v Final velocity
g Acceleration due to gravity
For these given inputs,
Outputs, Formulas
We calculate the following outputs:
Time of fall\(t = \)\( \frac{ v + \sqrt{ v ^2 - 2 g h } }{ g } \)
Initial velocity\(u = \)\( v - g \cdot t \)
Calculator InputsSet #7
t Time of fall
u Initial velocity
h Height
For these given inputs,
Outputs, Formulas
We calculate the following outputs:
Acceleration due to gravity\(g = \)\( \frac{ 2 \cdot ( h - u \cdot t ) }{ t ^2 } \)
Final velocity\(v = \)\( u + g \cdot t \)
Examples
1
Consider that a person dropped an object from the top of a building with an initial velocity of 4 m/s. The object travelled for 10 s before touching the ground. What is the final velocity of object, and height of the building?
Answer
Given:
Time of fall, t = 10 s
Initial velocity, u = 4 m/s
Acceleration due to gravity, g = 9.81 m/s²
Calculating final velocity (v)...
\( v = \) \( u + g \cdot t \)
\( v = \) \(4+9.81\times10\)
\( v = \) 102.1 m/s
Calculating height (h)...
\( h = \) \( u \cdot t + \frac{1}{2} g \cdot t ^2 \)
\( h = \) \(4\times10+ \frac{1}{2} \times9.81\times10^2 \)
\( h = \) 530.5 m
2
Consider that a person dropped an object from the top of a building with an initial velocity of 0 m/s. The object travelled for 2 s before touching the ground. What is the final velocity of object, and height of the building?
Answer
Given:
Time of fall, t = 2 s
Initial velocity, u = 0 m/s
Acceleration due to gravity, g = 9.81 m/s²
Calculating final velocity (v)...
\( v = \) \( u + g \cdot t \)
\( v = \) \(0+9.81\times2\)
\( v = \) 19.62 m/s
Calculating height (h)...
\( h = \) \( u \cdot t + \frac{1}{2} g \cdot t ^2 \)
\( h = \) \(0\times2+ \frac{1}{2} \times9.81\times2^2 \)
\( h = \) 19.62 m
3
Consider that a bird dropped a toy from top of an electric pole. The initial velocity of the toy is 4 m/s. The toy reached a final velocity of 20 m/s before touching the ground. What is the height of the pole, and time taken by the toy to reach the ground?
Answer
Given:
Final velocity, v = 20 m/s
Initial velocity, u = 4 m/s
Acceleration due to gravity, g = 9.81 m/s²
Calculating time of fall (t)...
\( t = \) \( \frac{ v - u }{ g } \)
\( t = \) \( \frac{20-4}{9.81} \)
\( t = \) 1.631 s
Calculating height (h)...
\( h = \) \( u \cdot \frac{ v - u }{ g } + \frac{1}{2} g \cdot \left( \frac{ v - u }{ g } \right)^2 \)
Consider that a bird dropped chicken lollipop from top of a building of height 50 m. Since, the bird slipped it, consider that initial velocity is 0 m/s. Calculate the time taken by the chicken lollipop to reach ground, and also its final velocity with which it makes contact with ground.
Answer
Given:
Height, h = 50 m
Initial velocity, u = 0 m/s
Acceleration due to gravity, g = 9.81 m/s²
Calculating time of fall (t)...
\( t = \) \( \frac{ - u + \sqrt{ u ^2 + 2 g h } }{ g } \)
The same bird throwed another chicken lollipop from top of another building. Consider that we somehow calculated the final velocity to be 50 m/s, time to reach the ground to be 5 s. Calculate the initial velocity of the chicken lollipop with which the bird has thrown it, and also height of the building.
Answer
Given:
Final velocity, v = 50 m/s
Time of fall, t = 5 s
Acceleration due to gravity, g = 9.81 m/s²
Calculating initial velocity (u)...
\( u = \) \( v - g \cdot t \)
\( u = \) \(50-9.81\times5\)
\( u = \) 0.95 m/s
Calculating height (h)...
\( h = \) \(( v - g \cdot t ) \cdot t + \frac{1}{2} g \cdot t ^2 \)
\( h = \) \((50-9.81\times5) \times5+ \frac{1}{2} \times9.81\times5^2 \)
\( h = \) 127.375 m
Input and Output Combinations of the Free Fall Calculator
Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.
Calculator InputsSet #1
t Time of fall
u Initial velocity
g Acceleration due to gravity
For these given inputs,
Outputs, Formulas
We calculate the following outputs:
Final velocity\(v = \)\( u + g \cdot t \)
Height\(h = \)\( u \cdot t + \frac{1}{2} g \cdot t ^2 \)
Initial velocity\(u = \)\( \frac{ h - \frac{1}{2} g \cdot t ^2 }{ t } \)
Final velocity\(v = \)\( \frac{ h + \frac{1}{2} g \cdot t^2 }{ t } \)
Calculator InputsSet #6
h Height
v Final velocity
g Acceleration due to gravity
For these given inputs,
Outputs, Formulas
We calculate the following outputs:
Time of fall\(t = \)\( \frac{ v + \sqrt{ v ^2 - 2 g h } }{ g } \)
Initial velocity\(u = \)\( v - g \cdot t \)
Calculator InputsSet #7
t Time of fall
u Initial velocity
h Height
For these given inputs,
Outputs, Formulas
We calculate the following outputs:
Acceleration due to gravity\(g = \)\( \frac{ 2 \cdot ( h - u \cdot t ) }{ t ^2 } \)
Final velocity\(v = \)\( u + g \cdot t \)
Examples
1
Consider that a person dropped an object from the top of a building with an initial velocity of 4 m/s. The object travelled for 10 s before touching the ground. What is the final velocity of object, and height of the building?
Answer
Given:
Time of fall, t = 10 s
Initial velocity, u = 4 m/s
Acceleration due to gravity, g = 9.81 m/s²
Calculating final velocity (v)...
\( v = \) \( u + g \cdot t \)
\( v = \) \(4+9.81\times10\)
\( v = \) 102.1 m/s
Calculating height (h)...
\( h = \) \( u \cdot t + \frac{1}{2} g \cdot t ^2 \)
\( h = \) \(4\times10+ \frac{1}{2} \times9.81\times10^2 \)
\( h = \) 530.5 m
2
Consider that a person dropped an object from the top of a building with an initial velocity of 0 m/s. The object travelled for 2 s before touching the ground. What is the final velocity of object, and height of the building?
Answer
Given:
Time of fall, t = 2 s
Initial velocity, u = 0 m/s
Acceleration due to gravity, g = 9.81 m/s²
Calculating final velocity (v)...
\( v = \) \( u + g \cdot t \)
\( v = \) \(0+9.81\times2\)
\( v = \) 19.62 m/s
Calculating height (h)...
\( h = \) \( u \cdot t + \frac{1}{2} g \cdot t ^2 \)
\( h = \) \(0\times2+ \frac{1}{2} \times9.81\times2^2 \)
\( h = \) 19.62 m
3
Consider that a bird dropped a toy from top of an electric pole. The initial velocity of the toy is 4 m/s. The toy reached a final velocity of 20 m/s before touching the ground. What is the height of the pole, and time taken by the toy to reach the ground?
Answer
Given:
Final velocity, v = 20 m/s
Initial velocity, u = 4 m/s
Acceleration due to gravity, g = 9.81 m/s²
Calculating time of fall (t)...
\( t = \) \( \frac{ v - u }{ g } \)
\( t = \) \( \frac{20-4}{9.81} \)
\( t = \) 1.631 s
Calculating height (h)...
\( h = \) \( u \cdot \frac{ v - u }{ g } + \frac{1}{2} g \cdot \left( \frac{ v - u }{ g } \right)^2 \)
Consider that a bird dropped chicken lollipop from top of a building of height 50 m. Since, the bird slipped it, consider that initial velocity is 0 m/s. Calculate the time taken by the chicken lollipop to reach ground, and also its final velocity with which it makes contact with ground.
Answer
Given:
Height, h = 50 m
Initial velocity, u = 0 m/s
Acceleration due to gravity, g = 9.81 m/s²
Calculating time of fall (t)...
\( t = \) \( \frac{ - u + \sqrt{ u ^2 + 2 g h } }{ g } \)
The same bird throwed another chicken lollipop from top of another building. Consider that we somehow calculated the final velocity to be 50 m/s, time to reach the ground to be 5 s. Calculate the initial velocity of the chicken lollipop with which the bird has thrown it, and also height of the building.
Answer
Given:
Final velocity, v = 50 m/s
Time of fall, t = 5 s
Acceleration due to gravity, g = 9.81 m/s²
Calculating initial velocity (u)...
\( u = \) \( v - g \cdot t \)
\( u = \) \(50-9.81\times5\)
\( u = \) 0.95 m/s
Calculating height (h)...
\( h = \) \(( v - g \cdot t ) \cdot t + \frac{1}{2} g \cdot t ^2 \)
\( h = \) \((50-9.81\times5) \times5+ \frac{1}{2} \times9.81\times5^2 \)
{
"topic": "free-fall",
"input_types": [
"float",
"float",
"float",
"float",
"float"
],
"input_labels": [
"u",
"t",
"g",
"v",
"h"
],
"input_descriptions": [
"Initial velocity",
"Time of fall",
"Acceleration due to gravity",
"Final velocity",
"Height"
],
"element_string": " of object",
"input_units": [
"m/s",
"s",
"m/s²",
"m/s",
"m"
],
"input_values": [
"0",
"",
"9.81",
"",
""
],
"formula_mathjax": "\\( v = u + g \\cdot t \\)<br>\\( h = u \\cdot t + \\frac{1}{2} g \\cdot t^2 \\)",
"input_pre_msg": "Enter any three inputs to calculate the other two values",
"type": "Calculate",
"title": "Free Fall Calculator",
"description": "Calculate the final velocity and height of an object in free fall using our Free Fall Calculator. Perfect for physics students, teachers, and enthusiasts.",
"category": "Kinematics",
"template": "physics",
"precision": 10,
"formulas": [
{
"parameters": [
"t",
"u",
"g"
],
"outputs": [
{
"label": "v",
"formula": " u + g * t ",
"formula_mathjax": "\\( u + g \\cdot t \\)",
"formula_mathjax_sub": "\\( u + g \\times t \\)"
},
{
"label": "h",
"formula": " u * t + 0.5 * g * Math.pow( t , 2 ) ",
"formula_mathjax": "\\( u \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)",
"formula_mathjax_sub": "\\( u \\times t + \\frac{1}{2} \\times g \\times t ^2 \\)"
}
],
"example_heading": "Consider that a person dropped an object from the top of a building with an initial velocity of _u_. The object travelled for _t_ before touching the ground.<br>What is the final velocity of object, and height of the building?",
"examples": [
{
"t": 10,
"u": 4,
"g": 9.81,
"v": "102.1",
"h": "530.5"
},
{
"t": 2,
"u": 0,
"g": 9.81,
"v": "19.62",
"h": "19.62"
}
]
},
{
"parameters": [
"v",
"u",
"g"
],
"outputs": [
{
"label": "t",
"formula": " ( v - u ) / g ",
"formula_mathjax": "\\( \\frac{ v - u }{ g } \\)"
},
{
"label": "h",
"formula": " u * ( v - u ) / g + 0.5 * g * Math.pow( ( v - u ) / g , 2 ) ",
"formula_mathjax": "\\( u \\cdot \\frac{ v - u }{ g } + \\frac{1}{2} g \\cdot \\left( \\frac{ v - u }{ g } \\right)^2 \\)",
"formula_mathjax_sub": "\\( u \\times \\frac{ v - u }{ g } + \\frac{1}{2} \\times g \\times \\left( \\frac{ v - u }{ g } \\right)^2 \\)"
}
],
"example_heading": "Consider that a bird dropped a toy from top of an electric pole. The initial velocity of the toy is _u_. The toy reached a final velocity of _v_ before touching the ground.<br>What is the height of the pole, and time taken by the toy to reach the ground?",
"examples": [
{
"v": 20,
"u": 4,
"g": 9.81,
"t": "1.631",
"h": "19.5719"
}
]
},
{
"parameters": [
"h",
"u",
"g"
],
"outputs": [
{
"label": "t",
"formula": " ( - u + Math.sqrt( Math.pow( u , 2 ) + 2 * g * h ) ) / g ",
"formula_mathjax": "\\( \\frac{ - u + \\sqrt{ u ^2 + 2 g h } }{ g } \\)",
"formula_mathjax_sub": "\\( \\frac{ - u + \\sqrt{ u ^2 + 2 \\times g \\times h } }{ g } \\)"
},
{
"label": "v",
"formula": " Math.sqrt( Math.pow( u , 2 ) + 2 * g * h ) ",
"formula_mathjax": "\\( \\sqrt{ u ^2 + 2 g h } \\)",
"formula_mathjax_sub": "\\( \\sqrt{ u ^2 + 2 \\times g \\times h } \\)"
}
],
"example_heading": "Consider that a bird dropped chicken lollipop from top of a building of height _h_. Since, the bird slipped it, consider that initial velocity is _u_.<br>Calculate the time taken by the chicken lollipop to reach ground, and also its final velocity with which it makes contact with ground.",
"examples": [
{
"h": 50,
"u": 0,
"g": 9.81,
"t": "3.1928",
"v": "31.3209"
}
]
},
{
"parameters": [
"v",
"t",
"g"
],
"outputs": [
{
"label": "u",
"formula": " v - g * t ",
"formula_mathjax": "\\( v - g \\cdot t \\)",
"formula_mathjax_sub": "\\( v - g \\times t \\)"
},
{
"label": "h",
"formula": " ( v - g * t ) * t + 0.5 * g * Math.pow( t , 2 ) ",
"formula_mathjax": "\\(( v - g \\cdot t ) \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)",
"formula_mathjax_sub": "\\(( v - g \\times t ) \\times t + \\frac{1}{2} \\times g \\times t ^2 \\)"
}
],
"example_heading": "The same bird throwed another chicken lollipop from top of another building. Consider that we somehow calculated the final velocity to be _v_, time to reach the ground to be _t_. <br>Calculate the initial velocity of the chicken lollipop with which the bird has thrown it, and also height of the building.",
"examples": [
{
"t": 5,
"v": 50,
"g": 9.81,
"u": "0.95",
"h": "127.375"
}
]
},
{
"parameters": [
"h",
"t",
"g"
],
"outputs": [
{
"label": "u",
"formula": " ( h - 0.5 * g * Math.pow( t , 2 ) ) / t ",
"formula_mathjax": "\\( \\frac{ h - \\frac{1}{2} g \\cdot t ^2 }{ t } \\)",
"formula_mathjax_sub": "\\( \\frac{ h - \\frac{1}{2} \\times g \\times t ^2 }{ t } \\)"
},
{
"label": "v",
"formula": " ( h + 0.5 * g * Math.pow( t , 2 ) ) / t ",
"formula_mathjax": "\\( \\frac{ h + \\frac{1}{2} g \\cdot t^2 }{ t } \\)",
"formula_mathjax_sub": "\\( \\frac{ h + \\frac{1}{2} \\times g \\times t ^2 }{ t } \\)"
}
]
},
{
"parameters": [
"h",
"v",
"g"
],
"outputs": [
{
"label": "t",
"formula": " ( v + Math.sqrt( Math.round( ( v * v - 2 * g * h ) * 100) / 100 ) ) / g ",
"formula_mathjax": "\\( \\frac{ v + \\sqrt{ v ^2 - 2 g h } }{ g } \\)",
"formula_mathjax_sub": "\\( \\frac{ v + \\sqrt{ v ^2 - 2 \\times g \\times h } }{ g } \\)"
},
{
"label": "u",
"formula": " v - g * t ",
"formula_mathjax": "\\( v - g \\cdot t \\)",
"formula_mathjax_sub": "\\( v - g \\times t \\)"
}
]
},
{
"parameters": [
"t",
"u",
"h"
],
"outputs": [
{
"label": "g",
"formula": " ( 2 * ( h - u * t ) ) / Math.pow( t , 2 ) ",
"formula_mathjax": "\\( \\frac{ 2 \\cdot ( h - u \\cdot t ) }{ t ^2 } \\)",
"formula_mathjax_sub": "\\( \\frac{ 2 \\times ( h - u \\times t ) }{ t ^2 } \\)"
},
{
"label": "v",
"formula": " u + g * t ",
"formula_mathjax": "\\( u + g \\cdot t \\)",
"formula_mathjax_sub": "\\( u + g \\times t \\)"
}
]
}
],
"content": "<h2>What is Free Fall?</h2><p>Free fall refers to the motion of an object falling under the influence of gravity alone, without any air resistance. The key parameters in free fall are time of fall (t), final velocity (v), height (h), initial velocity (u), and the acceleration due to gravity (g).</p><h2>Calculating Final Velocity and Height</h2><p>The <strong>final velocity</strong> of an object in free fall is calculated using the formula:</p><p class=\"formula_highlite\">\\( v = u + g \\cdot t \\).</p><p>The <strong>height</strong> from which the object falls is calculated using the formula:</p><p class=\"formula_highlite\">\\( h = u \\cdot t + \\frac{1}{2} g \\cdot t^2 \\).</p><br><h2>Input and Output Combinations of the Free Fall Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">t</span> Time of fall</li><li><span class=\"input\">u</span> Initial velocity</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Final velocity</span><span class=\"output\">\\(v = \\)\\( u + g \\cdot t \\)</span></li><li><span class=\"output_label\">Height</span><span class=\"output\">\\(h = \\)\\( u \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</span></li></ul><a class=\"button\" href=\"#example_1\">2 Examples</a></div><div class=\"formula_set set_2\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #2</span><ul class=\"given\"><li><span class=\"input\">v</span> Final velocity</li><li><span class=\"input\">u</span> Initial velocity</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Time of fall</span><span class=\"output\">\\(t = \\)\\( \\frac{ v - u }{ g } \\)</span></li><li><span class=\"output_label\">Height</span><span class=\"output\">\\(h = \\)\\( u \\cdot \\frac{ v - u }{ g } + \\frac{1}{2} g \\cdot \\left( \\frac{ v - u }{ g } \\right)^2 \\)</span></li></ul><a class=\"button\" href=\"#example_3\">1 Example</a></div><div class=\"formula_set set_3\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #3</span><ul class=\"given\"><li><span class=\"input\">h</span> Height</li><li><span class=\"input\">u</span> Initial velocity</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Time of fall</span><span class=\"output\">\\(t = \\)\\( \\frac{ - u + \\sqrt{ u ^2 + 2 g h } }{ g } \\)</span></li><li><span class=\"output_label\">Final velocity</span><span class=\"output\">\\(v = \\)\\( \\sqrt{ u ^2 + 2 g h } \\)</span></li></ul><a class=\"button\" href=\"#example_4\">1 Example</a></div><div class=\"formula_set set_4\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #4</span><ul class=\"given\"><li><span class=\"input\">v</span> Final velocity</li><li><span class=\"input\">t</span> Time of fall</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Initial velocity</span><span class=\"output\">\\(u = \\)\\( v - g \\cdot t \\)</span></li><li><span class=\"output_label\">Height</span><span class=\"output\">\\(h = \\)\\(( v - g \\cdot t ) \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</span></li></ul><a class=\"button\" href=\"#example_5\">1 Example</a></div><div class=\"formula_set set_5\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #5</span><ul class=\"given\"><li><span class=\"input\">h</span> Height</li><li><span class=\"input\">t</span> Time of fall</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Initial velocity</span><span class=\"output\">\\(u = \\)\\( \\frac{ h - \\frac{1}{2} g \\cdot t ^2 }{ t } \\)</span></li><li><span class=\"output_label\">Final velocity</span><span class=\"output\">\\(v = \\)\\( \\frac{ h + \\frac{1}{2} g \\cdot t^2 }{ t } \\)</span></li></ul></div><div class=\"formula_set set_6\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #6</span><ul class=\"given\"><li><span class=\"input\">h</span> Height</li><li><span class=\"input\">v</span> Final velocity</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Time of fall</span><span class=\"output\">\\(t = \\)\\( \\frac{ v + \\sqrt{ v ^2 - 2 g h } }{ g } \\)</span></li><li><span class=\"output_label\">Initial velocity</span><span class=\"output\">\\(u = \\)\\( v - g \\cdot t \\)</span></li></ul></div><div class=\"formula_set set_7\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #7</span><ul class=\"given\"><li><span class=\"input\">t</span> Time of fall</li><li><span class=\"input\">u</span> Initial velocity</li><li><span class=\"input\">h</span> Height</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Acceleration due to gravity</span><span class=\"output\">\\(g = \\)\\( \\frac{ 2 \\cdot ( h - u \\cdot t ) }{ t ^2 } \\)</span></li><li><span class=\"output_label\">Final velocity</span><span class=\"output\">\\(v = \\)\\( u + g \\cdot t \\)</span></li></ul></div></div><br><br><h2>Examples</h2>\n <div id=\"example_1\" class=\"example\">\n <span class=\"example_n\">1</span>\n <h3 class=\"question\">\n Consider that a person dropped an object from the top of a building with an initial velocity of <strong>4 m/s</strong>. The object travelled for <strong>10 s</strong> before touching the ground.<br>What is the final velocity of object, and height of the building?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Time of fall, t = 10 s</li><li>Initial velocity, u = 4 m/s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating final velocity (v)...</p><p class=\"step\">\\( v = \\) \\( u + g \\cdot t \\)</p><p class=\"step\">\\( v = \\) \\(4+9.81\\times10\\)</p><p class=\"step answer\">\\( v = \\) 102.1 m/s</p><p>Calculating height (h)...</p><p class=\"step\">\\( h = \\) \\( u \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</p><p class=\"step\">\\( h = \\) \\(4\\times10+ \\frac{1}{2} \\times9.81\\times10^2 \\)</p><p class=\"step answer\">\\( h = \\) 530.5 m</p>\n </div>\n \n <div id=\"example_2\" class=\"example\">\n <span class=\"example_n\">2</span>\n <h3 class=\"question\">\n Consider that a person dropped an object from the top of a building with an initial velocity of <strong>0 m/s</strong>. The object travelled for <strong>2 s</strong> before touching the ground.<br>What is the final velocity of object, and height of the building?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Time of fall, t = 2 s</li><li>Initial velocity, u = 0 m/s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating final velocity (v)...</p><p class=\"step\">\\( v = \\) \\( u + g \\cdot t \\)</p><p class=\"step\">\\( v = \\) \\(0+9.81\\times2\\)</p><p class=\"step answer\">\\( v = \\) 19.62 m/s</p><p>Calculating height (h)...</p><p class=\"step\">\\( h = \\) \\( u \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</p><p class=\"step\">\\( h = \\) \\(0\\times2+ \\frac{1}{2} \\times9.81\\times2^2 \\)</p><p class=\"step answer\">\\( h = \\) 19.62 m</p>\n </div>\n \n <div id=\"example_3\" class=\"example\">\n <span class=\"example_n\">3</span>\n <h3 class=\"question\">\n Consider that a bird dropped a toy from top of an electric pole. The initial velocity of the toy is <strong>4 m/s</strong>. The toy reached a final velocity of <strong>20 m/s</strong> before touching the ground.<br>What is the height of the pole, and time taken by the toy to reach the ground?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Final velocity, v = 20 m/s</li><li>Initial velocity, u = 4 m/s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating time of fall (t)...</p><p class=\"step\">\\( t = \\) \\( \\frac{ v - u }{ g } \\)</p><p class=\"step\">\\( t = \\) \\( \\frac{20-4}{9.81} \\)</p><p class=\"step answer\">\\( t = \\) 1.631 s</p><p>Calculating height (h)...</p><p class=\"step\">\\( h = \\) \\( u \\cdot \\frac{ v - u }{ g } + \\frac{1}{2} g \\cdot \\left( \\frac{ v - u }{ g } \\right)^2 \\)</p><p class=\"step\">\\( h = \\) \\(4\\times \\frac{20-4}{9.81} + \\frac{1}{2} \\times9.81\\times \\left( \\frac{20-4}{9.81} \\right)^2 \\)</p><p class=\"step answer\">\\( h = \\) 19.5719 m</p>\n </div>\n \n <div id=\"example_4\" class=\"example\">\n <span class=\"example_n\">4</span>\n <h3 class=\"question\">\n Consider that a bird dropped chicken lollipop from top of a building of height <strong>50 m</strong>. Since, the bird slipped it, consider that initial velocity is <strong>0 m/s</strong>.<br>Calculate the time taken by the chicken lollipop to reach ground, and also its final velocity with which it makes contact with ground.\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Height, h = 50 m</li><li>Initial velocity, u = 0 m/s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating time of fall (t)...</p><p class=\"step\">\\( t = \\) \\( \\frac{ - u + \\sqrt{ u ^2 + 2 g h } }{ g } \\)</p><p class=\"step\">\\( t = \\) \\( \\frac{ -0+ \\sqrt{0^2 + 2 \\times9.81\\times50} }{9.81} \\)</p><p class=\"step answer\">\\( t = \\) 3.1928 s</p><p>Calculating final velocity (v)...</p><p class=\"step\">\\( v = \\) \\( \\sqrt{ u ^2 + 2 g h } \\)</p><p class=\"step\">\\( v = \\) \\( \\sqrt{0^2 + 2 \\times9.81\\times50} \\)</p><p class=\"step answer\">\\( v = \\) 31.3209 m/s</p>\n </div>\n \n <div id=\"example_5\" class=\"example\">\n <span class=\"example_n\">5</span>\n <h3 class=\"question\">\n The same bird throwed another chicken lollipop from top of another building. Consider that we somehow calculated the final velocity to be <strong>50 m/s</strong>, time to reach the ground to be <strong>5 s</strong>. <br>Calculate the initial velocity of the chicken lollipop with which the bird has thrown it, and also height of the building.\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Final velocity, v = 50 m/s</li><li>Time of fall, t = 5 s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating initial velocity (u)...</p><p class=\"step\">\\( u = \\) \\( v - g \\cdot t \\)</p><p class=\"step\">\\( u = \\) \\(50-9.81\\times5\\)</p><p class=\"step answer\">\\( u = \\) 0.95 m/s</p><p>Calculating height (h)...</p><p class=\"step\">\\( h = \\) \\(( v - g \\cdot t ) \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</p><p class=\"step\">\\( h = \\) \\((50-9.81\\times5) \\times5+ \\frac{1}{2} \\times9.81\\times5^2 \\)</p><p class=\"step answer\">\\( h = \\) 127.375 m</p>\n </div>\n <br><h2>Input and Output Combinations of the Free Fall Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">t</span> Time of fall</li><li><span class=\"input\">u</span> Initial velocity</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Final velocity</span><span class=\"output\">\\(v = \\)\\( u + g \\cdot t \\)</span></li><li><span class=\"output_label\">Height</span><span class=\"output\">\\(h = \\)\\( u \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</span></li></ul><a class=\"button\" href=\"#example_1\">2 Examples</a></div><div class=\"formula_set set_2\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #2</span><ul class=\"given\"><li><span class=\"input\">v</span> Final velocity</li><li><span class=\"input\">u</span> Initial velocity</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Time of fall</span><span class=\"output\">\\(t = \\)\\( \\frac{ v - u }{ g } \\)</span></li><li><span class=\"output_label\">Height</span><span class=\"output\">\\(h = \\)\\( u \\cdot \\frac{ v - u }{ g } + \\frac{1}{2} g \\cdot \\left( \\frac{ v - u }{ g } \\right)^2 \\)</span></li></ul><a class=\"button\" href=\"#example_3\">1 Example</a></div><div class=\"formula_set set_3\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #3</span><ul class=\"given\"><li><span class=\"input\">h</span> Height</li><li><span class=\"input\">u</span> Initial velocity</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Time of fall</span><span class=\"output\">\\(t = \\)\\( \\frac{ - u + \\sqrt{ u ^2 + 2 g h } }{ g } \\)</span></li><li><span class=\"output_label\">Final velocity</span><span class=\"output\">\\(v = \\)\\( \\sqrt{ u ^2 + 2 g h } \\)</span></li></ul><a class=\"button\" href=\"#example_4\">1 Example</a></div><div class=\"formula_set set_4\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #4</span><ul class=\"given\"><li><span class=\"input\">v</span> Final velocity</li><li><span class=\"input\">t</span> Time of fall</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Initial velocity</span><span class=\"output\">\\(u = \\)\\( v - g \\cdot t \\)</span></li><li><span class=\"output_label\">Height</span><span class=\"output\">\\(h = \\)\\(( v - g \\cdot t ) \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</span></li></ul><a class=\"button\" href=\"#example_5\">1 Example</a></div><div class=\"formula_set set_5\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #5</span><ul class=\"given\"><li><span class=\"input\">h</span> Height</li><li><span class=\"input\">t</span> Time of fall</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Initial velocity</span><span class=\"output\">\\(u = \\)\\( \\frac{ h - \\frac{1}{2} g \\cdot t ^2 }{ t } \\)</span></li><li><span class=\"output_label\">Final velocity</span><span class=\"output\">\\(v = \\)\\( \\frac{ h + \\frac{1}{2} g \\cdot t^2 }{ t } \\)</span></li></ul></div><div class=\"formula_set set_6\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #6</span><ul class=\"given\"><li><span class=\"input\">h</span> Height</li><li><span class=\"input\">v</span> Final velocity</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Time of fall</span><span class=\"output\">\\(t = \\)\\( \\frac{ v + \\sqrt{ v ^2 - 2 g h } }{ g } \\)</span></li><li><span class=\"output_label\">Initial velocity</span><span class=\"output\">\\(u = \\)\\( v - g \\cdot t \\)</span></li></ul></div><div class=\"formula_set set_7\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #7</span><ul class=\"given\"><li><span class=\"input\">t</span> Time of fall</li><li><span class=\"input\">u</span> Initial velocity</li><li><span class=\"input\">h</span> Height</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Acceleration due to gravity</span><span class=\"output\">\\(g = \\)\\( \\frac{ 2 \\cdot ( h - u \\cdot t ) }{ t ^2 } \\)</span></li><li><span class=\"output_label\">Final velocity</span><span class=\"output\">\\(v = \\)\\( u + g \\cdot t \\)</span></li></ul></div></div><br><br><h2>Examples</h2>\n <div id=\"example_1\" class=\"example\">\n <span class=\"example_n\">1</span>\n <h3 class=\"question\">\n Consider that a person dropped an object from the top of a building with an initial velocity of <strong>4 m/s</strong>. The object travelled for <strong>10 s</strong> before touching the ground.<br>What is the final velocity of object, and height of the building?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Time of fall, t = 10 s</li><li>Initial velocity, u = 4 m/s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating final velocity (v)...</p><p class=\"step\">\\( v = \\) \\( u + g \\cdot t \\)</p><p class=\"step\">\\( v = \\) \\(4+9.81\\times10\\)</p><p class=\"step answer\">\\( v = \\) 102.1 m/s</p><p>Calculating height (h)...</p><p class=\"step\">\\( h = \\) \\( u \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</p><p class=\"step\">\\( h = \\) \\(4\\times10+ \\frac{1}{2} \\times9.81\\times10^2 \\)</p><p class=\"step answer\">\\( h = \\) 530.5 m</p>\n </div>\n \n <div id=\"example_2\" class=\"example\">\n <span class=\"example_n\">2</span>\n <h3 class=\"question\">\n Consider that a person dropped an object from the top of a building with an initial velocity of <strong>0 m/s</strong>. The object travelled for <strong>2 s</strong> before touching the ground.<br>What is the final velocity of object, and height of the building?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Time of fall, t = 2 s</li><li>Initial velocity, u = 0 m/s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating final velocity (v)...</p><p class=\"step\">\\( v = \\) \\( u + g \\cdot t \\)</p><p class=\"step\">\\( v = \\) \\(0+9.81\\times2\\)</p><p class=\"step answer\">\\( v = \\) 19.62 m/s</p><p>Calculating height (h)...</p><p class=\"step\">\\( h = \\) \\( u \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</p><p class=\"step\">\\( h = \\) \\(0\\times2+ \\frac{1}{2} \\times9.81\\times2^2 \\)</p><p class=\"step answer\">\\( h = \\) 19.62 m</p>\n </div>\n \n <div id=\"example_3\" class=\"example\">\n <span class=\"example_n\">3</span>\n <h3 class=\"question\">\n Consider that a bird dropped a toy from top of an electric pole. The initial velocity of the toy is <strong>4 m/s</strong>. The toy reached a final velocity of <strong>20 m/s</strong> before touching the ground.<br>What is the height of the pole, and time taken by the toy to reach the ground?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Final velocity, v = 20 m/s</li><li>Initial velocity, u = 4 m/s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating time of fall (t)...</p><p class=\"step\">\\( t = \\) \\( \\frac{ v - u }{ g } \\)</p><p class=\"step\">\\( t = \\) \\( \\frac{20-4}{9.81} \\)</p><p class=\"step answer\">\\( t = \\) 1.631 s</p><p>Calculating height (h)...</p><p class=\"step\">\\( h = \\) \\( u \\cdot \\frac{ v - u }{ g } + \\frac{1}{2} g \\cdot \\left( \\frac{ v - u }{ g } \\right)^2 \\)</p><p class=\"step\">\\( h = \\) \\(4\\times \\frac{20-4}{9.81} + \\frac{1}{2} \\times9.81\\times \\left( \\frac{20-4}{9.81} \\right)^2 \\)</p><p class=\"step answer\">\\( h = \\) 19.5719 m</p>\n </div>\n \n <div id=\"example_4\" class=\"example\">\n <span class=\"example_n\">4</span>\n <h3 class=\"question\">\n Consider that a bird dropped chicken lollipop from top of a building of height <strong>50 m</strong>. Since, the bird slipped it, consider that initial velocity is <strong>0 m/s</strong>.<br>Calculate the time taken by the chicken lollipop to reach ground, and also its final velocity with which it makes contact with ground.\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Height, h = 50 m</li><li>Initial velocity, u = 0 m/s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating time of fall (t)...</p><p class=\"step\">\\( t = \\) \\( \\frac{ - u + \\sqrt{ u ^2 + 2 g h } }{ g } \\)</p><p class=\"step\">\\( t = \\) \\( \\frac{ -0+ \\sqrt{0^2 + 2 \\times9.81\\times50} }{9.81} \\)</p><p class=\"step answer\">\\( t = \\) 3.1928 s</p><p>Calculating final velocity (v)...</p><p class=\"step\">\\( v = \\) \\( \\sqrt{ u ^2 + 2 g h } \\)</p><p class=\"step\">\\( v = \\) \\( \\sqrt{0^2 + 2 \\times9.81\\times50} \\)</p><p class=\"step answer\">\\( v = \\) 31.3209 m/s</p>\n </div>\n \n <div id=\"example_5\" class=\"example\">\n <span class=\"example_n\">5</span>\n <h3 class=\"question\">\n The same bird throwed another chicken lollipop from top of another building. Consider that we somehow calculated the final velocity to be <strong>50 m/s</strong>, time to reach the ground to be <strong>5 s</strong>. <br>Calculate the initial velocity of the chicken lollipop with which the bird has thrown it, and also height of the building.\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Final velocity, v = 50 m/s</li><li>Time of fall, t = 5 s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating initial velocity (u)...</p><p class=\"step\">\\( u = \\) \\( v - g \\cdot t \\)</p><p class=\"step\">\\( u = \\) \\(50-9.81\\times5\\)</p><p class=\"step answer\">\\( u = \\) 0.95 m/s</p><p>Calculating height (h)...</p><p class=\"step\">\\( h = \\) \\(( v - g \\cdot t ) \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</p><p class=\"step\">\\( h = \\) \\((50-9.81\\times5) \\times5+ \\frac{1}{2} \\times9.81\\times5^2 \\)</p><p class=\"step answer\">\\( h = \\) 127.375 m</p>\n </div>\n <br><h2>Input and Output Combinations of the Free Fall Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">t</span> Time of fall</li><li><span class=\"input\">u</span> Initial velocity</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Final velocity</span><span class=\"output\">\\(v = \\)\\( u + g \\cdot t \\)</span></li><li><span class=\"output_label\">Height</span><span class=\"output\">\\(h = \\)\\( u \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</span></li></ul><a class=\"button\" href=\"#example_1\">2 Examples</a></div><div class=\"formula_set set_2\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #2</span><ul class=\"given\"><li><span class=\"input\">v</span> Final velocity</li><li><span class=\"input\">u</span> Initial velocity</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Time of fall</span><span class=\"output\">\\(t = \\)\\( \\frac{ v - u }{ g } \\)</span></li><li><span class=\"output_label\">Height</span><span class=\"output\">\\(h = \\)\\( u \\cdot \\frac{ v - u }{ g } + \\frac{1}{2} g \\cdot \\left( \\frac{ v - u }{ g } \\right)^2 \\)</span></li></ul><a class=\"button\" href=\"#example_3\">1 Example</a></div><div class=\"formula_set set_3\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #3</span><ul class=\"given\"><li><span class=\"input\">h</span> Height</li><li><span class=\"input\">u</span> Initial velocity</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Time of fall</span><span class=\"output\">\\(t = \\)\\( \\frac{ - u + \\sqrt{ u ^2 + 2 g h } }{ g } \\)</span></li><li><span class=\"output_label\">Final velocity</span><span class=\"output\">\\(v = \\)\\( \\sqrt{ u ^2 + 2 g h } \\)</span></li></ul><a class=\"button\" href=\"#example_4\">1 Example</a></div><div class=\"formula_set set_4\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #4</span><ul class=\"given\"><li><span class=\"input\">v</span> Final velocity</li><li><span class=\"input\">t</span> Time of fall</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Initial velocity</span><span class=\"output\">\\(u = \\)\\( v - g \\cdot t \\)</span></li><li><span class=\"output_label\">Height</span><span class=\"output\">\\(h = \\)\\(( v - g \\cdot t ) \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</span></li></ul><a class=\"button\" href=\"#example_5\">1 Example</a></div><div class=\"formula_set set_5\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #5</span><ul class=\"given\"><li><span class=\"input\">h</span> Height</li><li><span class=\"input\">t</span> Time of fall</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Initial velocity</span><span class=\"output\">\\(u = \\)\\( \\frac{ h - \\frac{1}{2} g \\cdot t ^2 }{ t } \\)</span></li><li><span class=\"output_label\">Final velocity</span><span class=\"output\">\\(v = \\)\\( \\frac{ h + \\frac{1}{2} g \\cdot t^2 }{ t } \\)</span></li></ul></div><div class=\"formula_set set_6\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #6</span><ul class=\"given\"><li><span class=\"input\">h</span> Height</li><li><span class=\"input\">v</span> Final velocity</li><li><span class=\"input\">g</span> Acceleration due to gravity</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Time of fall</span><span class=\"output\">\\(t = \\)\\( \\frac{ v + \\sqrt{ v ^2 - 2 g h } }{ g } \\)</span></li><li><span class=\"output_label\">Initial velocity</span><span class=\"output\">\\(u = \\)\\( v - g \\cdot t \\)</span></li></ul></div><div class=\"formula_set set_7\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #7</span><ul class=\"given\"><li><span class=\"input\">t</span> Time of fall</li><li><span class=\"input\">u</span> Initial velocity</li><li><span class=\"input\">h</span> Height</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Acceleration due to gravity</span><span class=\"output\">\\(g = \\)\\( \\frac{ 2 \\cdot ( h - u \\cdot t ) }{ t ^2 } \\)</span></li><li><span class=\"output_label\">Final velocity</span><span class=\"output\">\\(v = \\)\\( u + g \\cdot t \\)</span></li></ul></div></div><br><br><h2>Examples</h2>\n <div id=\"example_1\" class=\"example\">\n <span class=\"example_n\">1</span>\n <h3 class=\"question\">\n Consider that a person dropped an object from the top of a building with an initial velocity of <strong>4 m/s</strong>. The object travelled for <strong>10 s</strong> before touching the ground.<br>What is the final velocity of object, and height of the building?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Time of fall, t = 10 s</li><li>Initial velocity, u = 4 m/s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating final velocity (v)...</p><p class=\"step\">\\( v = \\) \\( u + g \\cdot t \\)</p><p class=\"step\">\\( v = \\) \\(4+9.81\\times10\\)</p><p class=\"step answer\">\\( v = \\) 102.1 m/s</p><p>Calculating height (h)...</p><p class=\"step\">\\( h = \\) \\( u \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</p><p class=\"step\">\\( h = \\) \\(4\\times10+ \\frac{1}{2} \\times9.81\\times10^2 \\)</p><p class=\"step answer\">\\( h = \\) 530.5 m</p>\n </div>\n \n <div id=\"example_2\" class=\"example\">\n <span class=\"example_n\">2</span>\n <h3 class=\"question\">\n Consider that a person dropped an object from the top of a building with an initial velocity of <strong>0 m/s</strong>. The object travelled for <strong>2 s</strong> before touching the ground.<br>What is the final velocity of object, and height of the building?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Time of fall, t = 2 s</li><li>Initial velocity, u = 0 m/s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating final velocity (v)...</p><p class=\"step\">\\( v = \\) \\( u + g \\cdot t \\)</p><p class=\"step\">\\( v = \\) \\(0+9.81\\times2\\)</p><p class=\"step answer\">\\( v = \\) 19.62 m/s</p><p>Calculating height (h)...</p><p class=\"step\">\\( h = \\) \\( u \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</p><p class=\"step\">\\( h = \\) \\(0\\times2+ \\frac{1}{2} \\times9.81\\times2^2 \\)</p><p class=\"step answer\">\\( h = \\) 19.62 m</p>\n </div>\n \n <div id=\"example_3\" class=\"example\">\n <span class=\"example_n\">3</span>\n <h3 class=\"question\">\n Consider that a bird dropped a toy from top of an electric pole. The initial velocity of the toy is <strong>4 m/s</strong>. The toy reached a final velocity of <strong>20 m/s</strong> before touching the ground.<br>What is the height of the pole, and time taken by the toy to reach the ground?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Final velocity, v = 20 m/s</li><li>Initial velocity, u = 4 m/s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating time of fall (t)...</p><p class=\"step\">\\( t = \\) \\( \\frac{ v - u }{ g } \\)</p><p class=\"step\">\\( t = \\) \\( \\frac{20-4}{9.81} \\)</p><p class=\"step answer\">\\( t = \\) 1.631 s</p><p>Calculating height (h)...</p><p class=\"step\">\\( h = \\) \\( u \\cdot \\frac{ v - u }{ g } + \\frac{1}{2} g \\cdot \\left( \\frac{ v - u }{ g } \\right)^2 \\)</p><p class=\"step\">\\( h = \\) \\(4\\times \\frac{20-4}{9.81} + \\frac{1}{2} \\times9.81\\times \\left( \\frac{20-4}{9.81} \\right)^2 \\)</p><p class=\"step answer\">\\( h = \\) 19.5719 m</p>\n </div>\n \n <div id=\"example_4\" class=\"example\">\n <span class=\"example_n\">4</span>\n <h3 class=\"question\">\n Consider that a bird dropped chicken lollipop from top of a building of height <strong>50 m</strong>. Since, the bird slipped it, consider that initial velocity is <strong>0 m/s</strong>.<br>Calculate the time taken by the chicken lollipop to reach ground, and also its final velocity with which it makes contact with ground.\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Height, h = 50 m</li><li>Initial velocity, u = 0 m/s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating time of fall (t)...</p><p class=\"step\">\\( t = \\) \\( \\frac{ - u + \\sqrt{ u ^2 + 2 g h } }{ g } \\)</p><p class=\"step\">\\( t = \\) \\( \\frac{ -0+ \\sqrt{0^2 + 2 \\times9.81\\times50} }{9.81} \\)</p><p class=\"step answer\">\\( t = \\) 3.1928 s</p><p>Calculating final velocity (v)...</p><p class=\"step\">\\( v = \\) \\( \\sqrt{ u ^2 + 2 g h } \\)</p><p class=\"step\">\\( v = \\) \\( \\sqrt{0^2 + 2 \\times9.81\\times50} \\)</p><p class=\"step answer\">\\( v = \\) 31.3209 m/s</p>\n </div>\n \n <div id=\"example_5\" class=\"example\">\n <span class=\"example_n\">5</span>\n <h3 class=\"question\">\n The same bird throwed another chicken lollipop from top of another building. Consider that we somehow calculated the final velocity to be <strong>50 m/s</strong>, time to reach the ground to be <strong>5 s</strong>. <br>Calculate the initial velocity of the chicken lollipop with which the bird has thrown it, and also height of the building.\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Final velocity, v = 50 m/s</li><li>Time of fall, t = 5 s</li><li>Acceleration due to gravity, g = 9.81 m/s²</li></ul>\n <p>Calculating initial velocity (u)...</p><p class=\"step\">\\( u = \\) \\( v - g \\cdot t \\)</p><p class=\"step\">\\( u = \\) \\(50-9.81\\times5\\)</p><p class=\"step answer\">\\( u = \\) 0.95 m/s</p><p>Calculating height (h)...</p><p class=\"step\">\\( h = \\) \\(( v - g \\cdot t ) \\cdot t + \\frac{1}{2} g \\cdot t ^2 \\)</p><p class=\"step\">\\( h = \\) \\((50-9.81\\times5) \\times5+ \\frac{1}{2} \\times9.81\\times5^2 \\)</p><p class=\"step answer\">\\( h = \\) 127.375 m</p>\n </div>\n "
}
ConvertOnline