On a vacation in Puerto Rico rose jumped off a cliff into a river in El Yunque go forest reserve her height as a function of time could be modeled by the function h(t) = -16tequals -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

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cristoshiwa cristoshiwa · Answer 1 · 2020-04-20T04:32:40+02:00

Answer: t = 6 s

Step-by-step explanation:

When Rose hit the water, the height of the jump is 0, so: h(t) = 0.

Resolving it, we have:

-16t² + 16t + 480 = 0

To simplify the second degree equation, divided it by 16:

-t² + t + 30 = 0

Now, solve the equation using Bhaskara:

Δ = 1² - 4. (-1) . 30

Δ = 1 + 120

Δ = 121

t = [tex]\frac{-1+\sqrt{121} }{-2}[/tex]

t₁ = [tex]\frac{-1 + 11}{-2}[/tex] = - 5

t₂ = [tex]\frac{-11-11}{-2}[/tex] = 6

Since time can be negative, it took t = 6s for Rose to hit the water.