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

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.