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Multivariable Motion: Marbles Roll off Table, what is speed?

  1. Oct 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Two marbles roll off a table at the same moment. One of the marbles has a horizontal speed of 1 inch per second, and the other has a horizontal speed of 4 inches per second.
    a) Which marble hits the ground first?
    b) If the table surface is 3 feet from the ground, what are the speeds of the marbles as they hit?

    2. Relevant equations

    Don't know, as I can not use normal physics equations to solve for this problem (as my calc professor never mentioned/ used the physics equations to solve such problems in this chapter). Some how derivatives and integrals come into play..

    3. The attempt at a solution

    a) The marble traveling 4 inches per second hits the ground first. I say this out of common sense though, so I am wondering if there is any mathematical way to figure this out?

    b) No idea how to solve for this as we can't use physics equations.
     
  2. jcsd
  3. Oct 7, 2012 #2

    ehild

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    Do the marbles start from the same distance to the edge of the table?

    ehild
     
  4. Oct 8, 2012 #3
    Yes they do
     
  5. Oct 8, 2012 #4

    Ray Vickson

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    Are you claiming that you are not ALLOWED to use standard physical laws? If so, what *are* you allowed to use? (It is a shame that your "solution" violates several hundred years worth of physical experience.)

    RGV
     
  6. Oct 8, 2012 #5

    ehild

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    The question: what is meant with the sentence that the marbles roll off the table at the same moment. If they start rolling on the table from the same distance to the edge, the fastest reaches the edge and starts to fall earlier than the other one. In this case the faster one reaches the ground first. But they both fall for the same time. If they really roll off at the same time, they reach the ground at the same time again.
    The motion of the falling balls can be decomposed into a horizontal and vertical component. In the horizontal direction, the ball moves with constant velocity: dx/dt=c (constant). In the vertical direction, the ball moves downwards with constant acceleration: d2y/dt2=g=9.8 m/s2. You see, the vertical motion is not connected to the horizontal velocity. Find dy/dt and y in terms of t. You know that the change of y is 3 feet. Find the time of fall. From that, calculate the vertical velocity when hitting the ground. The vertical and horizontal velocities add up as vectors: the speed is the magnitude of the velocity vector.

    ehild
     
    Last edited: Oct 8, 2012
  7. Oct 8, 2012 #6

    Ray Vickson

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    My interpretation of the phrase "roll off a table at the same moment" would be that they become airborne at exactly the same time.

    RGV
     
  8. Oct 8, 2012 #7

    ehild

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    I think the same, but I tried to find a situation when the faster marble reaches the ground first.

    ehild
     
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