uploaded imageTwo masses (M and M) are attached to the ends of a massless rigid rod. The rod is mounted on an axle (the axis of rotation is the z axis) through the center; the two masses are both at distance R from the axle. The masses and rod are initially at rest.
A third mass m, with initial velocity v0 [^(j)], will collide head on with the mass M on the right, as shown. The collision is perfectly elastic. After the collision the mass m will either continue moving in the same direction or it will bounce back and move in the -y direction.

(A) Determine the final speed of m.
(B) Find the condition on the masses such that the mass m bounces backward.
(C) Determine the final angular velocity on the rod.
[[Hint: What quantities are constants of the motion?]]

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