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Transfer of momentum problem?

Here's an interesting puzzle:

The whole scenario takes place in one dimension of space.

Ball B is at rest. Ball A moves with momentum [tex]p_a[/tex]

Ball A makes a perfectly elastic head-on collision with Ball B. Ball B moves off with momentum [tex]p_b[/tex]


Prove that [tex]|\frac{p_b}{p_a}|<2[/tex]

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