A river of width d flows with speed v. A swimmer can swim with speed u relative to water, where u > v. He wants to reach the point directly opposite on the other bank. The time required is:
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Question

A river of width d flows with speed v. A swimmer can swim with speed u relative to water, where u > v. He wants to reach the point directly opposite on the other bank. The time required is:

G1 Physics · Accepted Answer

To reach directly opposite, the upstream component of swimmer velocity must cancel the river: uₓ = v. Hence the cross-river component is uᵧ = √(u² - v²). Therefore t = d/uᵧ = d/√(u² - v²).

A river of width d flows with speed v. A swimmer can swim with speed u relative to water, where u &gt; v. He wants to reach the point directly opposite on the other bank. The time required is:

A river of width d flows with speed v. A swimmer can swim with speed u relative to water, where u > v. He wants to reach the point directly opposite on the other bank. The time required is: