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

Question

Mathematics

Marisol Burns

16 November, 23:20

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

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Micah Horne · Answer 1

H (t) = - 16t² + 16 t + 480

Factor out - 16

-16 (t² - t - 30)

t² - t - 30

(t + 5) (t - 6) ⇒ t (t-6) + 5 (t-6) ⇒ t² - 6t + 5t - 30 ⇒ t² - t - 30

t + 5 = 0 t - 6 = 0

t = - 5 t = 6

The value of t is either - 5 or 6 however time can't be measured in negative form; then, it took Rose 6 seconds to hit the water.