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Momentum and Relative Velocity

  1. Nov 5, 2009 #1
    1. The problem statement, all variables and given/known data
    A 56-kg woman contestant on a reality television show is at rest at the south end of a horizontal 141-kg raft that is floating in crocodile-infested waters. She and the raft are initially at rest. She needs to jump from the raft to a platform that is several meters off the north end of the raft. She takes a running start. When she reaches the north end of the raft she is running at 4.0 m/s relative to the raft. At that instant, what is her velocity relative to the water?

    2. Relevant equations

    p=person w=water r=raft
    Vp = Vpr + Vrw

    m*v(i) = m*v(f)

    3. The attempt at a solution

    Using conservation of momentum
    0 = 56 * 4 + Vr*141
    Solving for Vr = -1.59 m/s

    Vp = 4-1.59 = 2.41 m/s which is apparently wrong and I cannot see why it would be, any help would be appreciated
  2. jcsd
  3. Nov 6, 2009 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    The momentum of the woman + raft does not change. Therefore:

    [tex]m_p\vec{v_{p:w}} + m_r\vec{v_{r:w}} = 0[/tex]

    where the :w means the velocity relative to the water.

    To find the velocity of the woman relative to the water you have to use the relation:

    [tex]\vec{v_{p:r}} + \vec{v_{r:w}} = \vec{v_{p:w}}[/tex]

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