To cross a river along the shortest path, a swimmer aims at angle θ with the upstream direction. What is the ratio of the minimum possible crossing time to the time taken while crossing along the shortest-distance path? Assume swimmer speed exceeds river speed.
Options

Question

To cross a river along the shortest path, a swimmer aims at angle θ with the upstream direction. What is the ratio of the minimum possible crossing time to the time taken while crossing along the shortest-distance path? Assume swimmer speed exceeds river speed.

Options

G1 Physics · Accepted Answer

Minimum time occurs when swimming perpendicular to the river, giving across speed v. For shortest-distance path, upstream component cancels flow and across component is v sinθ when θ is measured from upstream direction. Thus tₘᵢₙ/tshortest = (d/v)/(d/(v sinθ))=sinθ. Option B.