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Help with momentum problems?

  1. Jan 17, 2013 #1
    1. The problem statement, all variables and given/known data
    A comet of mass 6000 kg travelling at 30 000 m/s splits into two pieces that move apart with velocities that make equal angles of 20° relative to the original trajectory. If one piece is found to be 5 times the mass of the other...calculate the mass of each piece, find the impulse of the system, and calculate the velocities of the two pieces.



    2. Relevant equations
    P = mv
    P total before = P total after
    Impulse = ΔP



    3. The attempt at a solution
    Mass 1 = 1000 kg and Mass 2 = 5000kg

    i assumed that mass one travelled 20° above the horizontal, while mass two travelled 20° below the horizontal.

    So;

    P before = mv = (6000kg)(30 000 m/s) = 1.8 x 10^8 kg m/s [+x]

    P1 after = m1v1 = 1000v1 kg m/s [+x 20° +y]
    P1 after X = 1000(v1) kg m/s cos20° = 939.69(v1) [+x]
    P1 after Y = 1000(v1) kg m/s sin20° = 342.02(v1) [+y]

    P2 after = m2v2 = 5000v2 kg m/s [+x 20° -y]
    P2 after x = 5000(v2)cos20° = 4698.46(v2) [+x]
    P2 after y = 5000(v2)sin20° = 1710(v2) [-y]

    Vector Equations
    x: 1.8 x 10^8 kg m/s = 939.69(v1) + 4698.46(v2)
    y: 0 = 342.02(v1) - 1710(v2)

    I'm not sure how to solve for the velocities at this point, any help is appreciated.
    Thank you!
     
    Last edited: Jan 17, 2013
  2. jcsd
  3. Jan 17, 2013 #2

    gneill

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    Staff: Mentor

    Two equations, two unknowns...
     
  4. Jan 17, 2013 #3
    I'm allowed to use substitution even though they're in different axis?
     
  5. Jan 17, 2013 #4

    gneill

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    Staff: Mentor

    Yup. V1 and V2 are independent variables that appear in both equations and must have the same values in each!
     
  6. Jan 17, 2013 #5
    Ahh! Thank you so much :)
     
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