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 ?=45degrees with the line from A to C

To swim directly from A to B, what speed us, relative to the water, should the swimmer have?

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 ? = 45 degrees with the line from A to C To swim directly from A to B, what speed us, relative to the water, should the swimmer have?

Explanation / Answer

u:velocity relative to water, ux: x-component, uy:y-component

ux=uy=u/sqrt(2) [because theta=45 deg]

time taken to travel d1=d1/uy

distance in x direction travelled in that time: d2=(vr-ux)*d1/uy

=>150=(5-ux)*200/ux

=>3ux=20-4ux=>ux=20/7

ux=uy=u/sqrt(2)

therefore, u=ux*sqrt(2)=20/7*sqrt(2)=4.04 m/s

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