Table of Contents
Calculating Fall Time
The time it takes an object to fall from a given height is determined by the height and gravitational acceleration. From rest, the time increases with the square root of height: doubling the height increases fall time by a factor of sqrt(2) = 1.414, not double. A 10-meter fall takes 1.43 seconds; 40 meters takes 2.86 seconds (exactly double the time for 4 times the height).
This calculation is fundamental in physics education and has practical applications in construction safety, sports timing, amusement park ride design, and accident investigation. The iconic "dropping things from towers" experiments have been used since Galileo to demonstrate gravitational principles.
Formula
Time Table
| Height (m) | Time (s) | Impact Speed |
|---|---|---|
| 1 | 0.45 | 4.4 m/s |
| 5 | 1.01 | 9.9 m/s |
| 20 | 2.02 | 19.8 m/s |
| 50 | 3.19 | 31.3 m/s |
| 100 | 4.52 | 44.3 m/s |
FAQ
Why does time increase with sqrt of height?
From d = 1/2*g*t^2, solving for t gives t = sqrt(2d/g). The square root means height must quadruple to double the fall time. This is because the object accelerates, covering more distance in each successive second.
How long is a skydiver in free fall?
Jumping from 4,000 m (typical sport skydive), free fall lasts about 60 seconds before parachute deployment at ~750 m. However, air resistance means the actual fall takes longer than the vacuum calculation would predict.
What is the "5-second rule" in geology?
To estimate cliff height, drop a rock and count seconds until impact. Height in meters = 5 * t^2 (approximately). A 3-second fall means about 45 meters (148 feet). This is a useful field estimation technique, though wind and sound delay introduce some error.