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

Question

1 month ago

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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

Mathematics

2 answers:

AnnZ [12.3K] · Answer 1 · 2026-03-31T15:53:03+03:00

It will take 6 seconds.

We can factor out -16 from the whole equation since all coefficients can be divided by 16:

0 = -16(t² - t - 30)

The remaining trinomial can be factored easily; the numbers -6 and 5 multiply to -30 and add to -1:[[-6(5) = -30 and -6 + 5 = -1]:

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

Using the zero product property yields either t+5=0 or t-6=0, which gives t=-5 or t=6. Since negative time is not applicable, we use t=6.

Leona [12.6K] · Answer 2 · 2026-03-31T15:50:59+03:00

H (t) = - 16t ^ 2 + 16t + 480
To address this, we first set the polynomial to zero to find its roots.
So we have:
0 = -16t ^ 2 + 16t + 480
This leads us to the roots of the polynomial:
t1 = -5
t2 = 6
We disregard the negative root since time cannot be less than zero.
Final answer:
Rose takes about
t = 6 seconds