Question

2. Alice and Bob are swimming in a river. They start together at the same point on the bank of a wide strcam that flows with a speed v. Both move at the same speed c (where c > v) relative to the water. Alice swims downstream a distance L and then upstream the same distance. Bob swims so that his motion relative to the Earth is perpendicular to the banks of the stream. He swims the distance L and then back the same distance, with both swimmers returning to the starting point. In terms of L, c, and v, find the time intervals required (a) for Alice's round trip. b for Bob's round trip (c) Explain which swimmer returns first. (Refer back to this calculation in physics 4C and 4D when you consider the Michclson interferometer and the Michelson-Morley experiment.)

Answer 1

a) velocity of a lice down stream = v + c distance traveled by the alice L time taken by alice downstream-td time taken by alice up stream tu- total time taken by a lice-T.-td + tu,-- 2Lc 2L b) time taken by the bob toswim front and back -TB- c) on comparing T and T 2L 2L since C - Hence Bob will returns first