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The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by:

1. 30° west
2. 0°
3. 60° west
4. 45° west

Correct answer: 60° west

Solution

To cross the river along the shortest path, the swimmer must counteract the eastward flow of the river. Using vector components, the angle θ is given by tan(θ) = river speed/swimmer speed = 10/20 = 1/2. Thus, θ = arctan(1/2) ≈ 26.57°, which rounds to 30° west of north.

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