A catapult launches a boulder with an upward velocity of 92 m/s. the height of the boulder, h, in meters after t seconds is given by the function h=-5t^2+92t+16. how long does it take to reach maximum height? what is the boulders maximum height?

Question

Physics

Nylah Pratt

9 June, 03:57

A catapult launches a boulder with an upward velocity of 92 m/s. the height of the boulder, h, in meters after t seconds is given by the function h=-5t^2+92t+16. how long does it take to reach maximum height? what is the boulders maximum height?

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Answers (1)

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Autumn Ritter · Answer 1

H = - 5 t² + 92 t + 16

h ' = - 10 t + 92

- 10 t + 92 = 0

10 t = 92

t = 92 : 10

t = 9.2 s

h max = - 5 · 9.2² + 92 · 9.2 + 16 = - 432.2 + 846.6 + 16 = 430.2 m

Answer: It will take 9.2 seconds to reach the maximum height of 430.2 m.