A river flows with speed v and a swimmer can swim with speed u relative to water, where v > u. He must cross the river and wants to minimize his downstream drift. If θ is the angle at which he swims upstream measured from the perpendicular to the bank, then:
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Question

A river flows with speed v and a swimmer can swim with speed u relative to water, where v > u. He must cross the river and wants to minimize his downstream drift. If θ is the angle at which he swims upstream measured from the perpendicular to the bank, then:

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G1 Physics · Accepted Answer

Drift x = (v - u sinθ)t and t = d/(u cosθ). Hence x = d(v - u sinθ)/(u cosθ). Differentiating with respect to θ and setting dx/dθ = 0 gives v sinθ - u = 0. Therefore sinθ = u/v. Since v > u, this angle is physically possible.

A river flows with speed v and a swimmer can swim with speed u relative to water, where v &gt; u. He must cross the river and wants to minimize his downstream drift. If θ is the angle at which he swims upstream measured from the perpendicular to the bank, then:

A river flows with speed v and a swimmer can swim with speed u relative to water, where v > u. He must cross the river and wants to minimize his downstream drift. If θ is the angle at which he swims upstream measured from the perpendicular to the bank, then: