A man swims a distance L downstream and returns the same distance upstream. His speed relative to water is u and stream speed is v, where u > v. His average speed for the complete trip is:
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Question

A man swims a distance L downstream and returns the same distance upstream. His speed relative to water is u and stream speed is v, where u > v. His average speed for the complete trip is:

G1 Physics · Accepted Answer

Downstream speed = u + v and upstream speed = u - v. Total time = L/(u + v) + L/(u - v) = 2Lu/(u² - v²). Total distance = 2L. Hence average speed = 2L ÷ [2Lu/(u² - v²)] = (u² - v²)/u.

A man swims a distance L downstream and returns the same distance upstream. His speed relative to water is u and stream speed is v, where u &gt; v. His average speed for the complete trip is:

A man swims a distance L downstream and returns the same distance upstream. His speed relative to water is u and stream speed is v, where u > v. His average speed for the complete trip is: