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Momentum of colliding billard balls

  1. Jul 7, 2011 #1
    1. The problem statement, all variables and given/known data

    A white billiard ball with mass mw = 1.43 kg is moving directly to the right with a speed of v = 3.29 m/s and collides elastically with a black billiard ball with the same mass mb = 1.43 kg that is initially at rest. The two collide elastically and the white ball ends up moving at an angle above the horizontal of θw = 21° and the black ball ends up moving at an angle below the horizontal of θb = 69°.
    http://smartphysics.com/images/content/mechanics/ch12/billiardballsnew2.png [Broken]

    I need to find the final speeds of the balls.

    2. Relevant equations

    Conservation of momentum

    3. The attempt at a solution

    What I tried already was having initial momentum equal to final momentum. And then splitting it into x and y components and solving for the unknown velocities and got 1.4 for the black one and 3.66 for the white one. I'm not sure where I went wrong. Please help.

    Here is some of my work:
    Since masses cancel out, I have
    for X: 3.92 + 0 = Vwcos21 + Vbcos69
    for y: 0 = Vwsin21 - Vbsin69
    Then solved for Vb, which I got 1.4, but it's wrong.
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jul 7, 2011 #2


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    Your method is fine. You just swapped two digits in the initial velocity.
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