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

Question

The distance s that an object falls is directly proportional to the square of the time t of the fall. If an object falls 16 feet in 1 second, how far will it fall in 3 seconds? How long will it take an object to fall 400 feet?

Answer 1

First, find the proportionality constant from one pair of time-distance values, and then use it to generate time-distance pairs for any other time.

 

s = kt²

16 = k(1)² ⇒ k = 16

s(t) = 16t²

 

s(3) = 16(3)² ft = 144 ft

 

400 ft = 16t²

t = √(400/16) s = 5 s