As an illustration of the principle of relativity in classical mechanics, consider the following generic collision: In inertial frame S, particle A (mass mA, velocity uA) hits particle B (mass mB, velocity uB). In the course of the collision some mass rubs off A and onto B, and we are left with particles C (mass mC, velocity vC) and D (mass mD, velocity uD). Assume that momentum (p ≡ mu) is conserved in S.

(a) Prove that momentum is also conserved in inertial frame S, which moves with velocity v relative to S. [Use Galileo's velocity addition rule--this is an entirely classical calculation. What must you assume about mass?]

(b) Suppose the collision is elastic in S; show that it is also elastic in S.