Free Fall Calculator
Free Fall Calculator solves for a missing variable in free fall motion (no air resistance) using initial height, final height, initial velocity, time, and gravity.
Enter known values (leave the unknown field blank):
Methodology Used in Free Fall Calculator
The calculator uses kinematic equations adapted for free fall (acceleration = \\(-g\\)):
1. \\( v = v_0 – g t \\)
2. \\( h = h_0 + v_0 t – \frac{1}{2} g t^2 \\)
3. \\( v^2 = v_0^2 – 2 g (h_0 – h) \\)
4. \\( h = h_0 + \frac{v + v_0}{2} t \\)
Where:
- \\( h_0 \\): Initial height (m)
- \\( h \\): Final height (m)
- \\( v_0 \\): Initial velocity (m/s, positive upward)
- \\( v \\): Final velocity (m/s)
- \\( g \\): Gravitational acceleration (m/s², positive)
- \\( t \\): Time (s)
The solver identifies the missing variable, selects the appropriate equation, and solves algebraically, showing each step.
Example Calculation
Sample Input
Initial Height = 50 m, Final Height = 0 m, Initial Velocity = 0 m/s, Gravity = 9.81 m/s², Time = ?
Step 1: Identify knowns: \\( h_0 = 50 \\), \\( h = 0 \\), \\( v_0 = 0 \\), \\( g = 9.81 \\), solve for \\( t \\).
Step 2: Select equation with \\( h_0 \\), \\( h \\), \\( v_0 \\), \\( g \\), and \\( t \\):
\\[ h = h_0 + v_0 t – \frac{1}{2} g t^2 \\]Step 3: Substitute values:
\\[ 0 = 50 + 0 \cdot t – \frac{1}{2} \cdot 9.81 \cdot t^2 \\] \\[ \frac{1}{2} \cdot 9.81 \cdot t^2 = 50 \\] \\[ t^2 = \frac{50 \cdot 2}{9.81} \approx 10.1937 \\] \\[ t = \sqrt{10.1937} \approx 3.19 \, \text{s} \\]Result: Time = 3.19 s.