A steel ball with a velocity of 2.7 m/s collides elastically with an identical stationary steel ball, and ends up going at a 40. degree angle with its original path. What is the direction of the other ball? What is the final velocity of each?
Conservation of Momentum along x axis: m1v1i = m1v1fcostheta1 + m2v2fcostheta2
Conservation of Momentum along y axis: 0 = -m1v11fsintheta1 + m2v2fsintheta2
Conservation of Kinetic Energy for Elastic Collisions: .5m1v1^2 = .5m1f1f^2 + .5m2v2f^2
It's confusing with all the subscripts, but in short: p1initial + p2initial = p1final + p2final and Kinitial=Kfinal.
The Attempt at a Solution
I recognize that the balls are identical; thus, the masses cancel out.
Using the third equation (Conservation of KE): .5 (2.7^2) = .5v1f^2 + .5v2f^2
Solving for v1f: v1f = sqrt(7.29-v2f^2) This is all I have.
According to the answer key:
The direction of the other ball is 50 degrees.
I realize that you need to combine all three equations and use substitution to solve for the velocities and direction, but I'm not sure how. Any help would be greatly appreciated. Thank you!