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The rod is attached and can frictionlessly slide on the purple track. The questioner specified that the collision is elastic. The first obvious error in this problem is that the direction and magnitude of the final velocity of the ball is impossible. If the ball carries off all the energy it came in with, the rod must end up with no energy. And, conservation of linear momentum in theydirection (not conserved in thexdirection) demands that the speed of the center of mass (COM) of the rod along the rail would be 15 m/s meaning it would not be rotating. And, the angular momentum relative to the COM of the incoming ball is equal and opposite that of the outgoing ball, so the rod would have to be rotating to conserve angular momentum. So I thought to simply redraw the picture but with the final ball velocity having unknown components (2 unknowns). Two other unknowns are the final speed of the COM and the angular velocity of the rod about the COM. However, I only can see three equations: conservation of energy, linear momentum, and angular momentum. I would welcome suggestions on how to solve this problem which does not seem like it should be unsolvable. I'm a little rusty on my Goldstein-level classical mechanics when constraints (rail) are present; maybe that's the key? (Incidentally, the questioner would like a more general solution for any initial angle of the rod, but that should be straightforward once I understand a specific example.)

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# I Collision of a ball with a rod on a track

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