Question

A skydiver free falls from a plane 200 feet above the ground. Which of the following equations could represent the height of the skydiver as a function of time?

1. h(t) = -16t2 + 200t

2. h(t) = t2 + 199

3. h(t) = -16(t - 3) + 200

4. h(t) = -16t2 + 200

Answer 1

Katie,

Once the skydiver reaches terminal velocity, then he will be falling with constant speed. The distance he falls in time t will then be d = (160 ft/s)·t. And his altitude above the ground (height h) will be his altitude when the parachute opened minus the distance he has fallen so we can write:

h = (3200 ft) - (160 ft/s)·t

As a point of interest, the time it will take him to fall all the way to the ground is t = (3200 ft)/(160 ft/s) = 20 s

Answer 2

h(t) = -16t^2 + 200

Explanation: