Crossing a River: Find Speed Needed to Swim from A to B

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To determine the speed needed for a swimmer to cross a river from point A to point B, the swimmer's velocity relative to the water must be calculated, considering the river's current. The swimmer's velocity makes a 45-degree angle with the line from A to C, and the current flows at 5 km/h. The solution involves vector addition and trigonometry to find the swimmer's required speed of 4.04 km/h relative to the water. The discussion emphasizes the importance of understanding the relationship between the swimmer's velocity, the current, and the resultant velocity with respect to the shore. The key takeaway is the need to apply vector principles to solve the problem effectively.
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Homework Statement


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?

Homework Equations


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

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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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.
 

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