The formula
h = ½ · g · t²
| Symbol | Quantity | Unit |
|---|---|---|
| h | Drop height | m |
| t | Time of fall | s |
| v | Speed on landing | m/s |
What it means
In free fall the only force is gravity, so everything accelerates at the same rate regardless of mass. The distance fallen grows with the square of the time, which is why the second second covers three times the ground of the first.
How to work it out by hand
- Distance is half of g times the time squared
- Landing speed is g times the time
- To find the time from a height, rearrange and take the square root
What is worth knowing
The rule that all objects fall at the same rate is exactly true only in a vacuum, and Galileo's insight was seeing past the air rather than measuring through it. In practice a feather and a hammer fall identically on the Moon and very differently here — a demonstration David Scott performed on Apollo 15. Air resistance grows with speed until it balances gravity, at which point the object stops accelerating: that is terminal velocity, about 200 km/h for a skydiver in a spread position.