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Homework Help: Quick linear momemtum problem.

  1. Mar 19, 2010 #1
    1. The problem statement, all variables and given/known data
    Two astronauts, one of mass 62 kg and the other 85 kg, are initially at rest in outer space.
    They then push each other apart. How far apart are they when the lighter astronaut has moved 5.0 m?

    2. Relevant equations
    Conservation of momentum.
    Pi = Pf
    P1i + P2i = P1f + P2f

    3. The attempt at a solution
    Pi = Pf
    P1i + P2i = P1f + P2f
    (62)(0) + (85)(0) = (62)Vf1 + (85)Vf2

    How do I solve for 2 unknowns when you can't cancel the masses out because the masses are different?
  2. jcsd
  3. Mar 19, 2010 #2


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    Gold Member

    When momentum is conserved, the center of mass does not accelerate, i.e. it keeps its initial velocity. In this case the velocity of the center of mass is initially zero, so it remains zero after the push. Can you use this information to your advantage?
  4. Mar 19, 2010 #3

    Filip Larsen

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    From conservation of momentum you are in this case able to express the speed (with sign) of one astronaut as a function of the speed of the other. Now you should be able to think about how these speeds relate to the distance each astronaut has moved and what that has got to do with the one distance you do know.
  5. Mar 19, 2010 #4
    Because you started at rest, you know that the net velocity is going to be 0. Try plugging in a velocity for the lighter astronaut...
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