A river of width d flows downstream with speed v. A swimmer of speed u relative to water starts from A and wants to reach B on the opposite bank, where B is a distance L downstream from the point directly opposite A. If θ is measured downstream from the perpendicular to the bank, the condition for a straight ground path from A to B is:
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Question

A river of width d flows downstream with speed v. A swimmer of speed u relative to water starts from A and wants to reach B on the opposite bank, where B is a distance L downstream from the point directly opposite A. If θ is measured downstream from the perpendicular to the bank, the condition for a straight ground path from A to B is:

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G1 Physics · Accepted Answer

Ground-velocity components are Vₓ = u sinθ + v along the river and Vᵧ = u cosθ across it. A straight path from A to B requires Vₓ/Vᵧ = L/d. Therefore (u sinθ + v)/(u cosθ) = L/d.