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Math Help - Antiderivative 44

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    Antiderivative 44

    Two balls are thrown upward from the edge of the cliff.
    The first is thrown with a speed of 48ft/s and the other is thrown a
    second later with a speed of 24 ft/s.
    Do the balls ever pass each other?
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  2. #2
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    Quote Originally Posted by camherokid View Post
    Two balls are thrown upward from the edge of the cliff.
    The first is thrown with a speed of 48ft/s and the other is thrown a
    second later with a speed of 24 ft/s.
    Do the balls ever pass each other?
    Yes.

    Let the origin be the point where the balls are thrown upward and set a +y direction upward.

    The first ball has the position equation:
    y = y0 + v0*t + (1/2)at^2
    y = 48t - 16t^2

    The second ball has a position equation:
    y = y0 + v0*(t - 1) + (1/2)a(t - 1)^2 <-- Since it is launched 1 s later.
    y = 24(t - 1) - 16(t - 1)^2
    y = -16t^2 + 56t - 40

    When do these two y values equal each other? When
    48t - 16t^2 = -16t^2 + 56t - 40

    -8t = -40

    t =5 s

    -Dan
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