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Calculating the velocity of an object down a varied slope inclined plane

  1. Aug 16, 2015 #1
    An object starts at a height of 5m. The initial incline is 63.4 deg. After moving 2m in the x direction, the incline decreases to 7.125 deg and the motion continues for an additional 8m in the x direction. What is the total time for the object to complete the path?


    2. Relevant equations
    The initial move downward is 4m in the y and 2m in the x direction. The second move is 1m in the y and 8m in the x direction.

    3. The attempt at a solution
    Tried to solve it separating the moves and adding the time together.
     
  2. jcsd
  3. Aug 16, 2015 #2

    mfb

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    That is a good approach. Where is the problem?
     
  4. Aug 16, 2015 #3
    We solved for the time in the x direction and the y direction to make sure they matched. For the first leg, they did, for the second leg they didn't.

    I took my kids to the math musuem in the city last week and we saw an exhibit that highlighted the fastest way down a gravitational field. We're trying to work out a simpler method by using segments.

    Thanks,

    Doug
     
  5. Aug 16, 2015 #4

    haruspex

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    Please post your working (or there's no way to tell where you went wrong).
     
  6. Aug 18, 2015 #5

    mfb

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    No finite number of segments will give the optimum. Adding more and more segments in the right way will always improve the time - with the ideal curve as limiting case.
     
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