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Math Help - velocity of a falling ball help

  1. #1
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    velocity of a falling ball help

    In our simple model of the fight of a ball, the height
    y above the foor at time t is

     y = V_{n}t-\frac{1}{2}gt^{2}



    where g is the acceleration due to gravity and vn is the velocity immediately after the nth
    bounce.

    The maximum height of the ball is reached when dy/dt = 0
    Find the time
    tmax at which this maximum occurs and the maximum height
    ymax
    that the ball reaches.


    I am really not sure how to do this, since I do not know what vn is?

     \frac{dy}{dt} = V_{n} -gt = 0

     V_{n} = gt

    dont know how to work ourt  y_{max}

    and  t_{max}



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  2. #2
    Super Member
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    Re: velocity of a falling ball help

    t_{max} is the time when the derivative is zero, and you found the equation V_n=gt for that. So you solve for t and get t_{max}=\frac{V_n}{g}. Then you plug in to y = V_{n}t-\frac{1}{2}gt^{2} to get the height at time t_{max}, which is y_{max}.

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