Physics

Free Fall with Air Resistance Calculator

Find falling speed and distance accounting for air resistance.

Terminal velocity

Time

Gravity (m/s²)

Calculated Output

Velocity 39.176

Distance fallen 109.15

Formula: v = v_t·tanh(g·t/v_t)

Step-by-Step Breakdown

1. Values used:

2. Terminal velocity = 55

3. Time = 5

4. Gravity = 9.81 m/s²

6. Velocity = 39.176

7. Distance fallen = 109.15

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The math behind it

v = v_t·tanh(g·t/v_t) and distance = (v_t²/g)·ln(cosh(g·t/v_t)). Speed approaches but never exceeds v_t.

v_t 55 m/s after 5 s → about 41.7 m/s, having fallen ~125 m.

What sets terminal velocity?

The balance of gravity and drag, depending on mass, area and drag coefficient.