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Homework Statement
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?
Homework 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)
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.