Table of Contents
Fall Velocity Basics
The velocity of a freely falling object increases linearly with time (v = v0 + gt) and with the square root of distance fallen (v = sqrt(v0^2 + 2gh)). Without air resistance, there is no speed limit. In practice, air drag limits falling objects to a terminal velocity that depends on mass, shape, and air density.
Understanding fall velocity is essential for safety engineering (fall protection systems must absorb specific kinetic energies), sports science (impact analysis), ballistics, and aerospace engineering. The energy at impact scales with the square of velocity, making even small velocity increases significantly more dangerous.
Formulas
Kinetic energy per unit mass = 1/2*v^2 (J/kg). Total kinetic energy = 1/2*m*v^2.
Velocity Table
| Time/Height | Velocity | km/h |
|---|---|---|
| 1 s / 4.9 m | 9.81 m/s | 35.3 |
| 2 s / 19.6 m | 19.6 m/s | 70.6 |
| 3 s / 44.1 m | 29.4 m/s | 105.9 |
| 5 s / 122.6 m | 49.1 m/s | 176.6 |
| 10 s / 490.5 m | 98.1 m/s | 353.2 |
FAQ
Why does velocity increase linearly with time but as sqrt of distance?
Gravity provides constant acceleration, so v increases linearly with time. But since the object covers more distance per second as it speeds up, the relationship between v and distance is nonlinear. From energy conservation: 1/2*v^2 = g*h, giving v = sqrt(2gh).
What is the velocity after falling 1 meter?
v = sqrt(2 * 9.81 * 1) = 4.43 m/s (16 km/h or 10 mph). This is roughly walking speed, yet a 1-meter fall can cause injury because the sudden deceleration creates large forces on the body upon impact.
How is fall velocity used in safety?
Fall protection standards (OSHA, EN 363) require harnesses to limit fall arrest force to 6 kN. The energy absorption system must dissipate kinetic energy based on fall distance and worker mass. Impact velocity directly determines the required energy absorption capacity of the fall arrest system.