Jon is launching rockets in an open field. The path of the rocket can be modeled by the quadratic function h (t) = - 16t^2 + 96t, where h (t) is the height in feet any time t in seconds. After how many seconds will the rocket reach a height of 80 feet for the second time?

Question

Mathematics

Chaz Preston

14 November, 10:10

Jon is launching rockets in an open field. The path of the rocket can be modeled by the quadratic function h (t) = - 16t^2 + 96t, where h (t) is the height in feet any time t in seconds. After how many seconds will the rocket reach a height of 80 feet for the second time?

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Answers (1)

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Branden Ponce · Answer 1

To solve the problem, substitute 80 feet to value of h (t). so given that

h (t) = - 16t^2 + 96t

so

h (t) = - 16t^2 + 96t = 80

-16t^2 + 96t - 80 = 0

divide the whole equation with - 16

(-16t^2 + 96t - 80 = 0) 1/-16

t^2 - 6t + 5 = 0

factor the quadratic equation

(t - 5) (t - 1) = 0

t = 5

t = 1

so the answer would be 5 s, because it the rocket will reach the 80 ft for the first time at 1 s