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22 January, 07:40

A ball is thrown into the air with an upward velocity of 48 ft/s. Its height h in feet after t seconds is given by the function h = - 16t^2 + 48t + 6. How long does it take the ball to reach its maximum height? What is the ball's maximum height?

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  1. 22 January, 08:01
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    So you have to find the velocity (or first derivative) from the position function of h=-16t^2+48t+6

    the velocity is - 32t+48 which you then have to set equal to 0 in order to find t

    -32t+48=0

    -32t=-48

    t=1.5

    you then take your t value and sub it back into your original position function

    -16 (1.5) ^2+48 (1.5) + 6 which will give you a maximum height of 42 feet

    so the time it takes is 1.5 seconds to reach a maximum height of 42 feet
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