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Conservation of momentum: Student walking on surfboard find resultant velocity

  1. May 14, 2012 #1
    1. The problem statement, all variables and given/known data
    A 55 kg student stands on a 4.6 kg surfboard moving at 2.0 m/s [E]. The student then walks with a velocity of 1.9 m/s [E] relative to the surfboard, relative to the water. Neglect Friction.

    Answer: 0.25 m/s[E]

    2. Relevant equations
    m1vi1 + m2vi2 = m1vf1 + m2vf2

    3. The attempt at a solution
    m1= 55kg
    m2= 4.6kg
    vi1= ?
    vi2= ?
    vf1= ?
    vf2= ?

    How do I solve this? Please help me set up variables. Please and Thank you!
     
  2. jcsd
  3. May 14, 2012 #2

    HallsofIvy

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    Solve what? You haven't stated a problem. You titled this "find resultant velocity", but resultant velocity of what? The student or the surfboard?

    You need to use "conservation of momentum". The initial momentum of the "student-surfboard" system is 0 and so remains 0. In particular, the center of mass of the system will not move. Where is the center of mass initially? How does the student's center of mass move relative to that? How does the surfboard's center of mass move?
     
  4. May 14, 2012 #3
    He wasn't clear, but he's trying to solve for the final velocity of the surf board, because that's the only variable that's not given.

    On the initial side of the equation, you have the student and surfboard moving together, so their velocity will be the same and their mass will be added. Using basic algebra, this turns m1vi1 + m2vi2 into vi(m1+m2).

    ^edit: surely the initial momentum isn't 0 except if it were measured by the student himself, but clearly this is a reference frame outside the system since the system's initial velocity is given as 2 m/s.
     
    Last edited: May 14, 2012
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