Table of Contents
Finding Fall Height
Often we need to determine the height from which an object was dropped, given either the time it took to fall or the speed at impact. This calculation reverses the standard free fall equations. From time: h = 1/2*g*t^2. From impact velocity: h = v^2/(2g). Both assume no air resistance and no initial velocity.
This calculation is used in accident reconstruction, forensic science, structural engineering, and sports physics. For example, determining the floor a window broke from based on the time a witness heard the impact, or estimating fall height from injury patterns in forensic investigations.
Formulas
Height Examples
| Impact Speed | Height | Equivalent |
|---|---|---|
| 5 m/s (18 km/h) | 1.27 m | Table height |
| 10 m/s (36 km/h) | 5.1 m | 2nd floor |
| 20 m/s (72 km/h) | 20.4 m | 6th floor |
| 44 m/s (160 km/h) | 100 m | 30th floor |
FAQ
How accurate is this without air resistance?
For falls under about 50 meters with dense objects, air resistance has minimal effect (error less than 5%). For longer falls or light objects, air drag significantly reduces actual impact speed below the calculated value, meaning the true height would be greater than calculated from speed alone.
How is this used in forensics?
Forensic investigators use fall height calculations to determine if injuries are consistent with stated fall heights. Impact speed and energy correlate with injury severity. The calculation helps distinguish between accidental falls, jumps, and other scenarios.
What height causes terminal velocity?
A skydiver reaches terminal velocity (~55 m/s) after falling about 450 meters (roughly 12-15 seconds). After this point, falling from higher makes no difference to impact speed, which is why falls from very tall buildings are no more lethal than from moderate heights (once terminal velocity is reached).