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, as indicated in the figure.

A) 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

We know the man need same time to across the vertical and horizontal directions of river, (t). We assume the lower reaches river and the other side of river are positive direction.
The man's velocity Us can be separated by Vx1 and Vy. Vx1 for horizontal. Vy for vertical.
The man's velocity angle is 45 degree, when we separated his Us to Vx and Vy. we can find they are equal. Vx1=Us*cos45, Vy=Us*sin45. (sin45=cos45) ,and his final Vx2 should be 5km/hour minus Vx1. (the direction of Vx is negative.the river speed-5km/hour is positive)
so,
0.200(km/hour)/Vy=0.150(km/hour)/Vx2.....
Vx2=5km/hour-Vx1.........................
Vy=Vx1(sin45/cos45)......................
combine these 3 equations, we get 0.200(km/hour)/Vy=0.150(km/hour)/(5(km/h...
finally, Vy is 2.857km/hour
Us=Vysin45=4.04km/hour

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