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Homework Help: Two Balls Colliding. Check my work please!

  1. Sep 24, 2010 #1
    [PLAIN]http://img178.imageshack.us/img178/4781/345b.jpg [Broken]

    So I said v=v0-gt, and at the highest point, v=0, so t=v0/g.
    I also said uy=u0sinx-gt, and ux=u0cosx.
    So at t=v0/g, both balls have to be at their highest pint, and when uy=0, t=u0sinx/g...so equating the two times, I find u0sinx=v0...which I guess is obvious without calculation.
    So uy0=v0, and ux0=v0cotx, and u0=v0/sinx.
    In this time, the left ball must travel d, so ux0*t=v0cotx*v0/g=v02cotx/g=d...
    I did some rearranging and found that v0=(d*g*tanx)1/2.
    Since u0=v0/sinx=(d*g*tanx)1/2/sinx, we need to minimize (tanx)1/2/sinx= (1/(sinxcosx))1/2...which is a minimum at x=45o, and when x=45o, v=(d*g)1/2.
    Is this right?
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 24, 2010 #2


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    Looks right to me.
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