Free Fall Height Calculator

Gravitational Acceleration (

g

Initial Velocity (

v_{0}

Time of Fall (

t

1. What is the Free Fall Height Calculator?

Definition: This calculator computes the height ( $H$ ) an object falls under free fall conditions, based on gravitational acceleration ( $g$ ), initial velocity ( $v_{0}$ ), and time of fall ( $t$ ).

Purpose: It is used in physics, engineering, and education to determine the distance fallen by an object under gravity.

2. How Does the Calculator Work?

The calculator uses the formula:

$H = v_{0} \cdot t + \frac{1}{2} g t^{2}$

Where:

$g$ : Gravitational acceleration (m/s², ft/s²);
$v_{0}$ : Initial velocity (m/s, km/h, ft/s, mph, kn, km/s, mi/s, ft/min, m/min);
$t$ : Time of fall (s, min);
$H$ : Height fallen (cm, m, km, in, ft, yd, mi).

Steps:

Enter the gravitational acceleration ( $g$ ) with its unit.
Enter the initial velocity ( $v_{0}$ ) with its unit.
Enter the time of fall ( $t$ ) with its unit.
Convert all inputs to base SI units (m/s² for $g$ , m/s for $v_{0}$ , s for $t$ ).
Calculate the height using $H = v_{0} \cdot t + \frac{1}{2} g t^{2}$ .
Convert the result to the selected output unit.
Display the result, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of Free Fall Height Calculation

Calculating free fall height is crucial for:

Physics Education: Understanding gravitational motion.
Engineering Safety: Designing fall protection systems.
Sports Science: Analyzing jumps and drops.

4. Using the Calculator

Example 1: Calculate the height fallen with $g = 9.81 {m/s}^{2}$ , $v_{0} = 0 m/s$ , and $t = 2 s$ :

Gravitational Acceleration: $g = 9.81 {m/s}^{2}$ ;
Initial Velocity: $v_{0} = 0 m/s$ ;
Time: $t = 2 s$ ;
Height: $H = 0 \cdot 2 + \frac{1}{2} \cdot 9.81 \cdot 2^{2} = 19.62 m$ ;
Result (in meters): $H = 19.6200 m$ .

Example 2: Calculate the height fallen with $g = 32.2 {ft/s}^{2}$ , $v_{0} = 10 km/h$ , and $t = 1 min$ :

Gravitational Acceleration: $g = 32.2 {ft/s}^{2} \times 0.3048 = 9.81856 {m/s}^{2}$ ;
Initial Velocity: $v_{0} = 10 km/h \times 0.277778 = 2.77778 m/s$ ;
Time: $t = 1 min \times 60 = 60 s$ ;
Height: $H = 2.77778 \cdot 60 + \frac{1}{2} \cdot 9.81856 \cdot 60^{2} = 166.6668 + 17673.648 = 17840.3148 m$ ;
Result (in feet): $H = 58530.0588 ft$ .

5. Frequently Asked Questions (FAQ)

Q: What is free fall height?
A: Free fall height is the distance an object falls under gravity, accounting for any initial velocity.

Q: What happens if the initial velocity is zero?
A: The formula simplifies to $H = \frac{1}{2} g t^{2}$ , as the object is dropped from rest.

Q: Does this calculator account for air resistance?
A: No, this calculator assumes ideal conditions with no air resistance.