Free Fall
Drop something from rest and get the fall time and the speed it hits the ground.
An object dropped from rest falls with time t = √(2h ÷ g) and lands at speed v = √(2gh), where g = 9.81 m/s². Drop it from 20 m and it falls for about 2.02 s, hitting the ground at roughly 19.8 m/s (about 71 km/h).
What free fall means
Free fall is motion under gravity alone, with no air resistance and no initial push. The object starts from rest, so its only acceleration is g ≈ 9.81 m/s² downward. Because that acceleration is constant, the same two relationships always hold: the fall time depends only on the height, and the impact speed depends only on the height (or, equivalently, on g times the time). This is a special case of the SUVAT equations of motion with initial velocity u = 0.
h = drop height, t = fall time, v = impact speed, g = 9.81 m/s² (drop from rest, no air resistance)
Worked example
Drop an object from a height of h = 20 m with g = 9.81 m/s²:
- 1 Find the fall time. t = √(2h ÷ g) = √(2 × 20 ÷ 9.81) = √4.077 ≈ 2.02 s.
- 2 Find the impact speed from the height. v = √(2gh) = √(2 × 9.81 × 20) = √392.4 ≈ 19.81 m/s.
- 3 Cross-check with v = g·t. v = g × t = 9.81 × 2.02 ≈ 19.81 m/s — the two routes agree.
Fall time and impact speed by drop height
Dropped from rest, g = 9.81 m/s², air resistance ignored.
| Height | Fall time | Impact speed |
|---|---|---|
| 1 m | 0.45 s | 4.43 m/s (16 km/h) |
| 5 m | 1.01 s | 9.90 m/s (36 km/h) |
| 10 m | 1.43 s | 14.01 m/s (50 km/h) |
| 20 m | 2.02 s | 19.81 m/s (71 km/h) |
| 50 m | 3.19 s | 31.32 m/s (113 km/h) |
| 100 m | 4.52 s | 44.29 m/s (159 km/h) |
Assumptions and limits
Air resistance is ignored. These formulas assume a vacuum. In real air, drag grows with speed and eventually limits the fall — a feather and a hammer only land together on the Moon.
Mass does not matter. The mass cancels out, so a bowling ball and a marble dropped together (in a vacuum) reach the ground at the same instant.
g varies slightly. We use g = 9.81 m/s², the standard value near Earth’s surface; it ranges from about 9.78 at the equator to 9.83 at the poles, and is far smaller on the Moon (≈ 1.62 m/s²).