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 = - 5t2 + 92t + 16. How long does it take to reach maximum height? What is the boulder's maximum height? Round to the nearest hundredth, if necessary. A. Reaches a maximum height of 16.00 meters in 18.4 seconds. B. Reaches a maximum height of 18.57 meters in 9.2 seconds. C. Reaches a maximum height of 37.14 meters in 18.4 seconds. D. Reaches a maximum height of 439.20 meters in 9.2 seconds.

Question

Physics

Jaydon Fox

5 December, 14:02

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 = - 5t2 + 92t + 16. How long does it take to reach maximum height? What is the boulder's maximum height? Round to the nearest hundredth, if necessary. A. Reaches a maximum height of 16.00 meters in 18.4 seconds. B. Reaches a maximum height of 18.57 meters in 9.2 seconds. C. Reaches a maximum height of 37.14 meters in 18.4 seconds. D. Reaches a maximum height of 439.20 meters in 9.2 seconds.

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Answers (1)

Know the Answer?

Eric Gutierrez · Answer 1

D. Reaches a maximum height of 439.20 meters in 9.2 seconds.

Explanation:

Given

h = - 5t² + 92t + 16

then

h' = 0 when the boulder reaches its maximum height

(-5t² + 92t + 16) ' = - 10t + 92 = 0

⇒ t = 92/10

⇒ t = 9.2 s

the maximum height will be

h = - 5 (9.2) ² + 92 (9.2) + 16

h = 439.20 m