A swimmer wants to cross a river, from point A to point B. as shown in the figur

Question

A swimmer wants to cross a river, from point A to point B. as shown in the figure. The distance d_1 (from A to C) is 200 m. the distance d_2 (from C to B) is 150 m, and the speed of the current in the river is 5 km/hour. Suppose that the swimmer's velocity relative to the water makes an angle of = 45 degrees with the line from A to C. as indicated in the figure. To swim directly from A to B, what speed. relative to the water, should the swimmer have? Express the swimmer's speed numerically, to three significant figures, in kilometers per hour.

Explanation / Answer

Here, (Vr - ussin(45))/uscos(45) = (150/200)

=> (5 -0.707us)/0.707us = 0.75

=> 5 -0.707us = 0.53us

=> us = 4.0412 km/hr   -----------------> swimmer speed relative to water

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