Expert: Bobby Soltani - 3/12/2006

Question
The distance an object falls is directly proportional to the square of the time it has been falling. After 6 seconds it has fallen 1296 feet. How long will it take to fall 2304 feet?

Answer
Hi Marie,

From the first sentence, we can write

D = a(t^2)

Where D is the distance, t is time, and a is a constant number.  We are told that the object falls 1296 ft in 6 seconds.  We can use this to solve for a.

1296 = a(6^2)

1296 = 36a
divide both sides by 36

a = 36

So, we can rewrite our equation as

D = 36*t^2

We want to know what t equals when D is 2304

2304 = 36*t^2

divide both sides by 36

t^2 = 64

Take the square root of both sides

t = 8 seconds.

Let me know if you have any questions.

Bobby