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7 November, 18:36

A toy rocket is shot vertically into the air from a launching pad 9 feet above the ground with an initial velocity of 168 feet per second. The height h, in

feet, of the rocket above the ground as t seconds after launch is given by the function h (t) = - 16t^2+168t+9. How long will it take the rocket to reach its maximum height? What is the maximum height?

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  1. 7 November, 21:59
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    Y (initial) = 9

    V (initial) = 168

    V (final) = 0

    g (accel-grav) = 32 (in feet per second

    squared)

    Use the following equation:

    V (final) = V (initial) + a (t)

    Since this object is moving straight up and

    down, a = - 32

    Enter the knowns into the equation

    0 = 168 - 32t

    32t = 168

    t = 168/9.8

    t = 5.25

    Now that you know the time it takes to

    reach it's maximum, use the general

    kinematics equation to solve for final

    distance:

    y (final) = y (initial) + V (initial) (t) + (1/2) a

    (t²)

    y (final) = 9 + 168 (5.25) + (1/2) (-32)

    (5.25²)

    = 9 + 882 - 441

    = 450 feet
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