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quiz 1 solution

quiz 1 solution - PHYS126 Quiz 1 Time 10min Name 1 Student...

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Unformatted text preview: PHYS126 Quiz 1 17-2-2011 Time: 10min Name: 1. Student ID: 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 Using classical velocity addition formula, (a) express t1 in terms of c, v and L (b) express t2 in terms of c, v and L (c) show in general, t1 = γ t 2 , where γ= 1 v2 1− 2 c You should draw vector diagrams to help your derivation and show your steps explicitly. Points will be given upon how well you present your answer. (Hint: Swimming across must be at an angle θ to balance the current flow, i.e. v = c sin θ) (10 marks) Solution to Quiz 1 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 (a) Along the water current, t1 = L L 2cL + =2 c + v c − v c − v2 2L c − v2 2 (b) Across the water current, t 2 = 2 2cL 2 t1 c 1 = c −v = = = γ , so t1 = γ t2 . (c) t 2 2 2L c −v v2 2 1− 2 c2 − v2 c ...
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