How far does a person fall without an arrest system in the first half-second?

In considering the distance a person falls in the first half-second without an arrest system, we can apply the principles of physics related to free fall. When an object is in free fall, it accelerates due to gravity, which is approximately 32 feet per second squared.

In the first half-second of fall, the velocity of the falling object is not constant but increases as it falls. At the beginning of the fall, the velocity is zero and, after half a second, the velocity can be calculated using the formula:

Velocity = Acceleration x Time

Where the acceleration due to gravity is 32 ft/s² and the time is 0.5 seconds. This results in a velocity of 16 ft/s after half a second.

To find the distance fallen in that time, we can use the formula:

Distance = Initial Velocity x Time + 0.5 x Acceleration x Time²

Since the initial velocity at the start of the fall is 0, the formula simplifies to:

Distance = 0.5 x 32 ft/s² x (0.5 s)² = 0.5 x 32 ft/s² x 0.25 s² = 0.5 x 8 ft