Let

'd' be the distance of the fall

't' is the time of the fall

Since d is proportional to the square of the time t we can write this down as

d = k * t^2 , where k is the coefficient of proportion

Lets find k.

We use the fact that for d = 16 feet the time t = 1 so we have

16 = k * 1^2

16 = k

k = 16

Now the equation for distance is d = 16 * t^2

How far will the object fall in 4 seconds?

For t = 4 s the distance will be d = 16 * 4^2 = 16 * 16 = 256 that is for 4 seconds the object falls 256 feet.

How long will it take an object to fall 400 feet?

This time d = 400 feet and we need to find t.

400 = 16 * t^2

16 * t^2 = 400

t^2 = 400 / 16

t^2 = 25

t = 25 ^ 0.5

t = 5 s

The object falls 400 feet in 5 seconds.