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Acrobat and monkey

  1. Sep 28, 2016 #1
    1. The problem statement, all variables and given/known data
    A circus acrobat of mass ##M## leaps straight up with initial velocity ##v_0## from the trampoline. As he rises up, he takes a trained monkey of mass ##m## off a perch at a height ##h## above the trampoline. What is the maximum height attained by the pair?

    2. Relevant equations


    3. The attempt at a solution

    This is a pretty simple problem. All we do is derive a new initial velocity from the conservation of momentum, and then calculate the h that results when the masses are combined. However, I am wondering why using the conservation of momentum is justified, since the system is not isolated because there is gravity acting in the y-direction. Thus, why can I use the conservation of momentum in the y-direction when the man and monkey collide?
     
  2. jcsd
  3. Sep 28, 2016 #2

    gneill

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    Staff: Mentor

    What is the assumption that is made for the time it takes for a collision to occur? What change in gravitational PE is expected over that time interval?
     
  4. Sep 28, 2016 #3
    Ah, okay. So in the very small limit of the time of collision momentum is conserved.
     
  5. Sep 28, 2016 #4

    gneill

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    Staff: Mentor

    Right. In particular, it occurs in a small enough time interval that there is no work done by gravity during the process as the objects don't move (noticeably) higher or lower in the gravitational field.
     
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