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1 December, 14:43

13. A catapult launches a boulder wint an upward velocity of 122 feet per second the height of the boulder (h) in feet after t seconds is given by the function h (t) = - 16t^2+122t+10. How long does it take the boulder to reach maximum height? What is the boulders maximum height? Round to the nearest hundredth if necessary.

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  1. 1 December, 14:49
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    For this case we have the following expression:

    h (t) = - 16t ^ 2 + 122t + 10

    We look for the maximum of the function, for this, we derive:

    h ' (t) = - 32t + 122

    We match zero:

    -32t + 122 = 0

    We cleared t:

    t = 122/32

    t = 3.8125 s

    Then, the maximum height will be:

    h (3.8125) = - 16 * (3.2185) ^ 2 + 122 * (3.2185) + 10

    h (3.8125) = 236.92 feet

    Answer:

    It takes the boulder to reach maximum height а bout:

    t = 3.8125 s

    the boulders maximum height is:

    236.92 feet
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