Verified answer

S = kt^2

2304 = 64k

k = 36

900 = 36t^2

t = 5 seconds

distance = K t^2 (directly proportional to the square of the time it has been falling)

at t = 8 sec ==> d = 2304

K = 2304/8^2 = 36 ft/s^2

when d = 900 ft

900 = 36 t^2

==> t = (900/36)^1/2

t= 5 seconds.

Hi Ben, this is a question requiring ratios. Here is a simple way to solve it:

Let:

a represent the time squared,

b represent the distance

c represent the time squared

d represent distance

We're trying to find c. We know everything else (s is just a symbol for seconds).

a/b = c/d

64(s²) / 2304ft = c² / 900ft

900*64/2304 = c²

c = √(25) seconds

c = 5 seconds

Therefore, it will take 5 seconds for the object to fall 900ft.

Hope this helps. Best of luck,

-Jessie

2304 : 8^2 :: 900 : t^2

whence t^2 = 900*8^2/2304 = 25 = 5^2

t = 5 seconds ANSWER