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17 July, 07:15

A ball is thrown up into the air with an initial velocity of 64 ft/sec. The ball is 4 ft above the ground when it is released. Its height, in feet, at time t seconds is given by: h (t) = - 16t^2 + 64t + 4. What is the time when it reaches its maximum height?

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  1. 17 July, 07:37
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    2 seconds and maximum height reached is 68 ft

    Explanation:

    h (t) = - 16t^2 + 64t + 4

    differentiate with respect to t

    h' (t) = - 32t + 64

    for maximum height velocity which is h' (t) must be zero

    -32t + 64 = 0

    -32t = - 64

    t = 2 s

    hence height is

    h (2) = - 16 (2) ^2 + 64 (2) + 4

    h (2) = - 64+128+4

    h (2) = 68 feet
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