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Conservation of momentum of a frog jump

  1. Mar 29, 2015 #1
    1. The problem statement, all variables and given/known data
    A frog of mass m jumps from the edge of a plank of mass M of length L to the other edge. The plank is on water and is free to move, assume no friction whatsoever. What is the minimum value of the speed of the frog ?

    2. Relevant equations
    Conservation of momentum and energy
    Some kinematics equations
    The answer given is sqrt((MgL)/(m+M))

    3. The attempt at a solution
    I think that the minimum speed means the magnitude of the velocity at the highest point, meaning Vx. But I cannot find
     
  2. jcsd
  3. Mar 29, 2015 #2

    gneill

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    Staff: Mentor

    What have you tried?

    Have you determined how far the frog must jump?
     
  4. Mar 29, 2015 #3
    Fix the end of plank without frog as (0,0) and let the frog be at (-L,0).
    What will happen when the frog jumps?
    What is center of mass of the system?
    Using the center of mass, calculate the distance the frog has to jump.
     
  5. Mar 29, 2015 #4

    haruspex

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    Gold Member
    2016 Award

    No, it means the minimum take-off speed. Remember that the frog can choose what angle to take off at.
     
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