The speed of a swimmer in still water is 20 m s⁻¹. The speed of river water is 10 m s⁻¹ and is flowing to 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 with respect to north is given by:
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Question

The speed of a swimmer in still water is 20 m s⁻¹. The speed of river water is 10 m s⁻¹ and is flowing to 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 with respect to north is given by:

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G1 Physics · Accepted Answer

Step 1: For the shortest path, the swimmer's ground velocity must be due north. Step 2: His westward component relative to water must cancel the 10 m s⁻¹ eastward river velocity. Step 3: If θ is west of north, 20 sinθ=10, so sinθ=1/2 and θ=30°. Final answer: D.