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3 February, 09:08

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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  1. 3 February, 11:02
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    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
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