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Find a curve such that time travel is minimum

  1. Oct 11, 2011 #1
    1. The problem statement, all variables and given/known data
    [PLAIN]http://vctson.com/temp/curve.jpeg [Broken]
    Find the curve y = f(x) so that the ball travels from A to B in minimum time?

    Thanks!
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Oct 11, 2011 #2
    What have you worked out thus far? You have to show some effort.
     
  4. Oct 11, 2011 #3
    I tried at some point on the curve, the gravity force goes down, then use 2nd Newton law. Thus, P = ma = my''. But, P = mg. It does not seem right and I can't find the relation y and x.
     
  5. Oct 11, 2011 #4
    Any hint? Thanks!
     
  6. Oct 11, 2011 #5
    this is the brachistochrone, so what is you kinetic and potential energy?

    solve in terms of v then seperate for ds/dt.

    ds = sqrt(dx^2 + dy^2)
     
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