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Math Help - The maximum height of a bouncing ball.

  1. #1
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    The maximum height of a bouncing ball.

    The maximum height of a bouncing ball.-bouncingballquestion.png
    My question is about b) which is asking for the maximum height. Attached as well is the solutions manual:
    The maximum height of a bouncing ball.-bouncingballsolution.png

    It did take me a while to understand a) but I see that as h goes to zero that b-32t is left so for now I have to accept it and move on.

    As for b) the solutions manual says that v(t) = 0 and that velocity is t =b/32.

    OK fine it must be the answer however at this point b is not known or is it? I tried graphing the equation b-32t however I am finding my graphing calculator only allows for one variable or maybe I just havn't figured out how to work another variable b in.

    The solutions manual goes on to describe s(b/32) = b^2/64 which also I am working on understanding but I just don't see how that was arrived at either.

    Perhaps I could get some explanation?

    Thanks in advance...

    P.S. I think both terms were multiplied by 1/32 and then solved for t to get b/32?
    Last edited by sepoto; October 27th 2013 at 01:56 AM.
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  2. #2
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    Re: The maximum height of a bouncing ball.

    Actually it looks more like the b/32 is the derivative solved for t. I could use some verification that is correct. It looks like this thing about b is all conceptual and is meant to apply to an equation with a real integer in place for b. I'm not sure about any of this yet.

    Hopefully I have the terminology correct when I refer to the derivative.
    Last edited by sepoto; October 27th 2013 at 06:30 AM.
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  3. #3
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    Re: The maximum height of a bouncing ball.

    The solution manual is correct.

    Quote Originally Posted by sepoto View Post
    OK fine it must be the answer however at this point b is not known or is it?
    Throughout this problem, b is a parameter, meaning that all quantities have to be expressed through b.

    Quote Originally Posted by sepoto View Post
    I tried graphing the equation b-32t however I am finding my graphing calculator only allows for one variable or maybe I just havn't figured out how to work another variable b in.
    You need to provide a concrete value of b; then you can graph it as a function of t.

    Quote Originally Posted by sepoto View Post
    The solutions manual goes on to describe s(b/32) = b^2/64 which also I am working on understanding but I just don't see how that was arrived at either.
    s(b/32) = b(b/32) - 16(b/32)^2 = b/32 - 16b/(32) = b/32 - b/(2*32) = b/32 - b/64 = b/64.
    Thanks from sepoto
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