1. The problem statement, all variables and given/known data A 20g ball is fired horizontally with initial speed vi toward a 100g ball that is hanging motionless from a 1.0m long string. The balls undergo a head-on, perfectly elastic collision after which the 100g ball swings out to a maximum angle of 50degrees. What was vi? 2. Relevant equations Conservation of momentum: m1vi1 + m2vi2 = m1vf1 + m2vf2 Conservation of energy: 1/2m1(vi1^2) = m2gy or 1/2m1(vi1^2) = m2gy + 1/2m1(vf1^2) 3. The attempt at a solution My prof says all the kinetic energy converts to potential gravitational energy, which I initially agreed with. My prof is consistently giving answers different from the book though. When I do it his way, I end up with an answer (5.9m/s) different from the book (7.9m/s). His way completely ignores the need for the conservation of momentum equation and, when I thought about it, the balls aren't equal mass so the shot ball should bounce back a little bit in addition to the larger ball swinging on the string. So I figured my conservation of energy equation should be the second one. When I do it this way though, I end up with all three velocities unknown from the conservation of momentum equation. With only two equations, I can't solve for the velocities. Can somebody point out to me where I've gone wrong? Thanks for any help.