Free Fall Calculator

Formulas

The formula to calculate the final velocity (v) of an object in free fall is:

\[ \text{v} = v₀ + g \cdot t \]

Where:

\(\text{v}\) is the final velocity (m/s)
\(v₀\) is the initial velocity (m/s)
\(g\) is the acceleration due to gravity (m/s²)
\(t\) is the total time (s)

The formula to calculate the total time of fall (t) is:

\[ t = \sqrt{\frac{2d}{g}} \]

Where:

\(t\) is the total time (s)
\(d\) is the distance traveled (height) (m)
\(g\) is the acceleration due to gravity (m/s²)

Free Fall Definition

Freefall is defined as the movement of an object under the influence of gravitational force only, with no other forces acting on it. In reality, air resistance would usually be present, but free-fall problems typically exclude this.

Example Calculation

Let's assume the following values:

Initial Velocity (v₀) = 0 m/s
Distance Traveled (d) = 20 meters
Acceleration due to Gravity (g) = 9.81 m/s²

Using the formula to calculate the total time of fall:

\[ t = \sqrt{\frac{2 \cdot 20}{9.81}} \approx 2.02 \text{ seconds} \]

Using the formula to calculate the final velocity:

\[ \text{v} = 0 + 9.81 \cdot 2.02 \approx 19.81 \text{ m/s} \]

The Total Time of Fall (t) is approximately 2.02 seconds.

The Final Velocity (v) is approximately 19.81 m/s.