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Unformatted text preview: Solution to Homework 1 Let c = speed of the swimmer in still water v = velocity of water current L = distance between starting and end points t1 = roundtrip time swimming along the river current t2 = roundtrip time across the river current Round trip of total distance 2L, along river Round trip of total distance 2L, across river Swimmer A, t1 Swimmer B, t2 Velocity of swimmer relative to water (magnitude c) Velocity of water relative to ground (magnitude v) Velocity of swimmer relative to ground For swimmer A, we have t1 = L L 2 Lc + =2 2 c+v c−v c −v For swimmer B, we have t2 =
So, L c −v
2 2 + L c −v
2 2 = 2L c2 − v2 2 Lc 2 2 t1 c 1 = c −v = = = γ , namely t1 = γ t2 2L t2 c2 − v2 v2 1− 2 c2 − v2 c ...
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