Free Fall Time Calculator

Gravitational Acceleration (\( g \)):

Initial Velocity (\( v_0 \)):

Height (\( h \)):

Velocity (\( v \)):

Time of Fall (\( t \)):

1. What is the Free Fall Time Calculator?

Definition: This calculator computes the time of fall (\( t \)) and final velocity (\( v \)) of an object in free fall based on gravitational acceleration (\( g \)), initial velocity (\( v_0 \)), and height (\( h \)).

Purpose: It is used in physics, engineering, and education to analyze the motion of objects under gravity.

2. How Does the Calculator Work?

The calculator uses the following kinematic equations:

\( v = \sqrt{v_0^2 + 2 g h} \)

\( t = \frac{v - v_0}{g} \)

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);
\( h \): Height (cm, m, km, in, ft, yd, mi);
\( v \): Final velocity (m/s, km/h, ft/s, mph, kn, km/s, mi/s, ft/min, m/min);
\( t \): Time of fall (s, min).

Steps:

Enter the gravitational acceleration (\( g \)) with its unit.
Enter the initial velocity (\( v_0 \)) with its unit.
Enter the height (\( h \)) with its unit.
Convert all inputs to base SI units (m/s² for \( g \), m/s for \( v_0 \), m for \( h \)).
Calculate the final velocity using \( v = \sqrt{v_0^2 + 2 g h} \).
Calculate the time using \( t = \frac{v - v_0}{g} \).
Convert the results to the selected output units.
Display the results, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of Free Fall Time and Velocity Calculation

Calculating free fall time and velocity is crucial for:

Physics Education: Understanding motion under gravity.
Engineering Safety: Designing fall protection systems.
Astronomy: Analyzing orbital mechanics.

4. Using the Calculator

Example 1: Calculate the time of fall and final velocity with \( g = 9.81 \, \text{m/s}^2 \), \( v_0 = 0 \, \text{m/s} \), \( h = 19.62 \, \text{m} \):

Gravitational Acceleration: \( g = 9.81 \, \text{m/s}^2 \);
Initial Velocity: \( v_0 = 0 \, \text{m/s} \);
Height: \( h = 19.62 \, \text{m} \);
Final Velocity: \( v = \sqrt{0^2 + 2 \cdot 9.81 \cdot 19.62} = \sqrt{384.9644} \approx 19.62 \, \text{m/s} \);
Time: \( t = \frac{19.62 - 0}{9.81} \approx 2 \, \text{s} \);
Result (Velocity in m/s): \( v = 19.6200 \, \text{m/s} \);
Result (Time in seconds): \( t = 2.0000 \, \text{s} \).

Example 2: Calculate the time of fall and final velocity with \( g = 32.2 \, \text{ft/s}^2 \), \( v_0 = 10 \, \text{ft/s} \), \( h = 100 \, \text{ft} \):

Gravitational Acceleration: \( g = 32.2 \, \text{ft/s}^2 \times 0.3048 = 9.81856 \, \text{m/s}^2 \);
Initial Velocity: \( v_0 = 10 \, \text{ft/s} \times 0.3048 = 3.048 \, \text{m/s} \);
Height: \( h = 100 \, \text{ft} \times 0.3048 = 30.48 \, \text{m} \);
Final Velocity: \( v = \sqrt{3.048^2 + 2 \cdot 9.81856 \cdot 30.48} = \sqrt{9.292 + 598.223} \approx 24.463 \, \text{m/s} \);
Time: \( t = \frac{24.463 - 3.048}{9.81856} \approx 2.185 \, \text{s} \);
Result (Velocity in ft/s): \( v = 80.2625 \, \text{ft/s} \);
Result (Time in minutes): \( t = 0.0364 \, \text{min} \).

5. Frequently Asked Questions (FAQ)

Q: What is free fall?
A: Free fall is the motion of an object under the influence of gravity alone, with no other forces (e.g., air resistance) acting on it.

Q: Why calculate both velocity and time?
A: Knowing both the final velocity and time of fall provides a complete picture of the object’s motion, useful for safety and design applications.

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