Word problem

Question

A window washer accidentally drops a bucket from the top of a 144-foot building. The height h of the bucket after t seconds  given by h=-16t²+144. When will the bucket hit the ground?

Answer 1

The bucket will hit the ground when its height (h) is 0. So, replace h with 0, and solve for t:

0=-16t²+144

Factor out the common term, -16:

0=-16(t²-9)

Factor t²-9:

0=-16(t-3)(t+3)

Set each of the terms t-3 and t+3 equal to 0, and solve:

t-3=0, so t=3 and t+3=0, so t=-3

So, we get two answers here. t=3 or -3 solves the equation. But, we are really only concerned with what happens AFTER we drop the bucket, so t=3 seconds makes the most sense.

 

Answer 2

It hits the ground when 

 

h(t) = 0.

 

-16t² + 144 = 0

 

t = √(144/16) sec = ? sec