Question

The distance an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 18 seconds?

a.
4536 ft
b.
5832 ft
c.
5184 ft
d.
288 ft

Answer 1

5184ft

Explanation:

d= distance an object falls when dropped from a tower

t= time it takes to fall

According to the first sentence,

d(sign of proportionality) t^2

Introducing a constant k:

d =kt^2

when d=144ft ,t=3sec

Substitute the values to find k

144 =k(3^2)

144 = 9k

k = 144/9

k =16

Substitute k =16 and t =18sec

d =kt^2

d =16×(18^2)

d =16× 324

d = 5184ft