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Consider a head-on elastic collision of a ‘bullet’ of rest-mass M with a stationary ‘target’ of...

Consider a head-on elastic collision of a ‘bullet’ of rest-mass M with a stationary ‘target’ of rest-mass m. Prove that the post-collision γ-factor of the bullet cannot exceed (m2+M2 )/(2Mm). This means that for large bullet energies (with γ-factors much larger than this critical value), the relative transfer of energy from bullet to target is almost total.

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