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Consider two skaters A and B initially a...

Consider two skaters `A` and `B` initially at rest on ice -(friction is negligible) with `A` holding a ball. A has greater mass than `B` and the ball has some significant mass. A throws the ball to `B`. `B` catches it and throws it back to `A` who catches it again. The magnitudes of the skater's (excluding ball) final velocities, A momentum and kinetic energies (denoted below as `v, p` and `K` respectively) are related as

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