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

second, how far will fall in 3 seconds? How long will it take an object to fall 400 feet?

Answer 1

144 feet

5 seconds

Explanation:

A directly proportional distance between s and t can be written as
s ∝ t²

or in equation form

s(t) = k · t²

k = constant of proportionality

Given s = 16 feet for t = 1 second we get

16 = k (1)²

or

k = 16

and the equation is s(t) = 16t²

In 3 seconds the object will fall
s(3) = 16 (3)²

= 16 x 9

= 144

s(3) = 144

To find time taken to fall 400 feet, substitute for s s(t) = 400

400 = 16t²

16t² = 400

t² = 400/16 = 25

t = ± √25 = ± 5 seconds

Since time is non-negatiive,

t = 5 seconds