Question

On a vacation in Puerto Rico, Rose jumped off a cliff into a river in EL Yunque Forest Reserve. Her height as a function of time could be modeled by the function 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

It would take 6 seconds.

We can factor -16 out of the entire equation, since all of the coefficients are divisible by 16:

0 = -16(t² - t - 30)

The remaining trinomial is easily factorable; factors of -30 that sum to -1 are -6 and 5 [-6(5) = -30 and -6 + 5 = -1]:

0 = -16(t+5)(t-6)

Using the zero product property, either t+5=0 or t-6=0; therefore t=-5 or t=6.  Since negative time makes no sense, t=6.

Answer 2

H (t) = - 16t ^ 2 + 16t + 480
 For this case, the first thing to do is to match the polynomial to zero to find the roots.
 We have then:
 0 = -16t ^ 2 + 16t + 480
 From here, we obtain the following roots of the polynomial:
 t1 = -5
 t2 = 6
 We ignore the negative root because the time is always greater than zero.
 Answer: 
 it takes Rose to hit the water about 
 t = 6 seconds