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 d1 (from A to C) is 200 m, the distance d2 (from C to B) is 150 m, and the speed vr of the current in the river is 5 km/hour. Suppose that the swimmer's velocity relative to the water makes an angle of theta = 45 degrees with the line from A to C, as indicated in the figure. To swim directly from A to B, what speed us, relative to the water, should the swimmer have? Express the swimmer's speed numerically, to three significant figures, in kilometers per hour.

Explanation / Answer

d1 = 200 m

d2 = 150 m

v_r = 5 km/h

theta = 45 deg

t = d2 / (v_r - u_s sin(theta)

t = d1 / ( u_s cos(theta) )

d2 / (v_r - u_s sin(theta) = d1 / ( u_s cos(theta) )

0.15 / ( 5 - u_s sin(45 deg) ) = 0.2 / (u_s cos(45 deg))

Solving we get

u_s = 4.04 km/h

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Speed of the swimmer = 4.04 km/hour

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