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Collision and using x and y coordinates.

  1. Nov 8, 2011 #1
    1. The problem statement, all variables and given/known data

    You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface. Sam, with mass 72.0 kg, is given a push and slides eastward. Abigail, with mass 54.0 kg, is sent sliding northward. They collide, and after the collision Sam is moving at 36.0 degrees north of east with a speed of 5.80 m/s and Abigail is moving at 15.0 degrees south of east with a speed of 8.80 m/s.

    Part A:
    What was the speed of each person before the collision?
    Sam's speed:
    Abigail speed:

    Part B:
    By how much did the total kinetic energy of the two people decrease during the collision?

    2. Relevant equations

    The momentum on initial x = momentum on final x

    The momentum on initial y = momentum on final y

    m1 = Sam, m2 = Abby
    mv = momentum


    3. The attempt at a solution

    on x:
    (72.0 kg)(unknown) + (54.0 kg)(0 m/s) = (72.0 kg)(5.80cos36)+(54.0 kg)(8.80 cos15)

    on y:

    (72.0 kg)(0)+(54.0 kg)(unknown) = (72.0 kg)(5.80sin36)+(54 kg)(8.80sin15)

    Sam = 11.067 m/s
    Abby = 6.823 m/s

    I also need help for Part B.

    Am I approaching this problem correctly? Thanks.
     
  2. jcsd
  3. Nov 8, 2011 #2
    Alright, I know Sam's initial velocity is 11.1 m/s for sure.

    I am doing something wrong when calculating Abby's initial velocity, but I'm not sure what.

    I did do (72.0 kg)(11.1 m/s) = (54.0 kg)(initial velocity) and received 14.8 m/s.

    I think this is right, however, I do not know how to calculate the answer the way I was suppose to(using y-coords).
     
    Last edited: Nov 8, 2011
  4. Nov 8, 2011 #3
    Check your signs, but your equations look correct. Since you have two equations and two unknowns it is a solvable system of equations. If you need helping solving the system, I would use substitution or you could try elimination.
     
  5. Nov 9, 2011 #4
    When I re-did the y-coords, I found that if I took 90 degrees minus the degrees given, then I would get 14.8 m/s.

    For example, sin15 should have been sin75, and sin 36 should have been sin56.

    Does this seem alright?
     
  6. Nov 9, 2011 #5
    I changed Abigail's final velocity to negative since it has direction. It worked.

    Thanks therealnihl.
     
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