# Crossing a river

1. Oct 11, 2009

### hover

1. The problem statement, all variables and given/known data
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 200m , the distance d_2 (from C to B) is 150m, and the speed v_r of the current in the river is 5 km/h. 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 u_s, relative to the water, should the swimmer have?

2. Relevant equations
I would think that you would use nothing more than some trig, Pythagorean theorem and stuff about adding and subtracting vectors

3. The attempt at a solution

I have no idea how to attempt this solution. I don't know where to even start. I know the answer is 4.04km/h but I have no idea how to get to that answer. Where should I start?

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2. Oct 11, 2009

### hover

Well don't all jump up at once now!

3. Oct 12, 2009

### Staff: Mentor

What direction must the swimmer's velocity have with respect to the shore? Hint: The velocity of the swimmer with respect to the shore = velocity of the swimmer with respect to the water + velocity of water with respect to the shore.