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Finding the velocity and angle after an elastic collision

  1. Jul 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Jerry and Mary, a young penguin couple, got separated because of an arctic storm. The storm is over and they start looking for each other. Jerry sees Mary first and he starts running on his little legs towards her. Then Mary sees Jerry and starts running as fast as she can toward him. There is ice all over so they end up sliding towards each other. Their precise directions are shown at the figure. When they meet they hug each other so tight that they keep sliding TOGETHER in a new direction, (COUNTERCLOCKWISE from the EAST), with a new speed, . What is and of the young penguin couple?



    Pix = initial momentum of the system in the x direction
    piy = initial momentum of the system in the y direction
    mj = mass of Jerry
    mm = mass of Mary
    Pfx = final momentum of the system in the x direction
    pfy = final momentum of the system in the y direction
    vf = final velocity of the system
    θf = final angle of the system
    vj = velocity of Jerry
    vm = velocity of Mary

    Data:

    ψj = 15°
    ψ = 10°

    mj = 5kg
    mm = 3kg

    vj = 1.2 m/s
    vm = 0.5 m/s

    Answer choices:
    A) =0.6m/s,θf = 287 CCW from the East.
    B) =1.1m/s, θf= 287 CCW from the East.
    C) =0.6m/s,θf = 163 CCW from the East.
    D) =1.1m/s,θf = 163 CCW from the East.
    E) =0.6m/s,θf = 253 CCW from the East.
    F) =1.1m/s,θf = 253 CCW from the East


    2. Relevant equations
    P =mv

    Conservation of momentum


    3. The attempt at a solution

    Pix in the x-direction= 5*1.2*sin(15) -2*0.5*sin(10)
    = 1.29244 kgm/s

    piy = 5*1.2*cos(15) - 3*0.5*cos(10)
    = 4.31834 kgm/s

    Initial velocity of the system = 5.61078 kgm/s

    Initial momentum = final momentum

    5.16 kgm/s = (5kg+3kg)Vf

    Vf = 0.7 m/s

    Did I make a mistake in my calculations? Is the 0.1 discrepancy due to a rounding difference?

    Then for the final angle:
    θf = arctan(4.31/1.29)
    = 73°

    Do I assume that the angle starts from the positive x-axis and moves clockwise? So I would get:
    360° - 73° = 287°
     

    Attached Files:

  2. jcsd
  3. Jul 28, 2012 #2

    CWatters

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    I haven't checked all your working but shouldn't that be 3*0.5*sin(10) in...

    Pix in the x-direction= 5*1.2*sin(15) -2*0.5*sin(10)

    EDIT. Ah it looks like you used 3 to get 1.29244 so that's not the problem.
     
  4. Jul 28, 2012 #3

    CWatters

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    Are you summing the vectors Pix and Piy correctly? (That's a hint not a question)
     
  5. Jul 28, 2012 #4
    I thought I had summed them correctly. I can see that I made a typo with
    5.16 kgm/s = (5kg+3kg)Vf

    which should be

    5.61 kgm/s = (5kg+3kg)Vf

    But the answer is still 0.7.
     
  6. Jul 28, 2012 #5

    CWatters

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