Question

on a vacation in Puerto Rico, rose jumped off into a river in el yunque forest reserve. her height as a function of time could be modeled by h(t)=-16t^2+16t+480, where t is the time after jumping in seconds and h is the height in feet. how many seconds did it take rose to hit the water? round your answer to the nearest hundredth

Answer 1

The main assumption here is that the height at the water level is 0.

So, the answer is given by the solution to the equation

- 16t^2 + 16t + 480 = 0

To solve it, start dividing by -16 to get:

t^2 - t - 30 = 0.

Now factor the left side:

(t -  ) (t +  ) =0

Find two numbers that add - 1 and its product is -30

(t -  6 ) (t + 5 ) =0

That gives:

t - 6 = 0 ⇒ t = 6 seconds

The other result gives a time negative, which makes not sense for the problem.

Verify substituing 6 in the original equation:

h(6) = -16*6^2 + 16*6 + 480 = -576 + 96 + 480 = 0. Lo cual confirma nuestra solucion.
 
It toke Rose 6 seconds to hit the water.