Momentum and Elastic Collisions

  1. 1. The problem statement, all variables and given/known data
    In a pool game, the cue ball, which has an initial speed of 8.0 m/s, make an elastic collision with the eight ball, which is initially at rest. After the collision, the eight ball moves at an angle of 30° to the original direction of the cue ball.

    2. Relevant equations
    V8 = Velocity of 8-ball
    Vc = Velocity of cue ball

    (1)Epx = m*V8*cos(30) + m*Vc*cos(x) = m*8
    (2)Epy = m*V8*sin(30) + m*Vc*sin(x) = 0
    (3).5*m*Vi^2 = .5*m*V8^2 + .5*m*Vc^2

    3. The attempt at a solution
    While these equations are technically solvable, they are nearly impossible by hand. Solving (3) for one velocity and using substitution twice I get:
    sin(x)^2 -cos(30)*cos(x) + sin(30)*cos(30)*cos(x) - sin(30)*cos(x)^2 = -1/8

    Is there an easier way to solve this since I know I will not be able to solve this equation myself?
  2. jcsd
  3. rl.bhat

    rl.bhat 4,435
    Homework Helper

    (1)Epx = m*V8*cos(30) + m*Vc*cos(x) = m*8
    (2)Epy = m*V8*sin(30) + m*Vc*sin(x) = 0

    Rewrite these two equations as
    m*V8*cos(30) = m*8 - m*Vc*cos(x) -------(1)
    m*V8*sin(30) = - m*Vc*sin(x) ----------(2)
    Square both sides of eq.1 and 2 and add them. After simplification you will get the value of vc*cos(x)
    From the conservation of energy equation, find the value of vc. Then you can find the angle x.
  4. Awesome, thanks so much!
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