Water now flows very slowly through the river bed, covering all but the tips of the islands. The water moves at speed u. You can't walk across the river any more, but must instead swim. Fortunately, you were on the Olympic swim team, and can swim at the same speed v that you normally walk.

When you try to swim directly across the river, you feel the current pulling you downstream. In order to move straight across from one bank to the other, you have to swim at an angle, pointed slightly upstream.

In fact, you have to point yourself just as shown in the figure at right, so that the ratio of your sideways to upstream speeds is v to u.

What is the hypotenuse of the triangle formed by these components of velocity?

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Write this value directly on the paper -- it will come in handy later.

Now, you aim your body upstream slightly and swim so that you go directly from A to B. How long does that trip take?

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How long will it take to swim back, from B to A? You'll need to swim at the same angle again.
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How long will it take to make the round trip?
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On the other hand, suppose you start on island X and swim downstream to the other island, Y. You go with the current. How long will that take?

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How long will it take to swim back against the current, from Y to X?
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How long will it take to make the round trip?
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Plug in some numbers: suppose that D = 2 km, v = 1 m/s, and u = 0.1 m/s. What are the times required for the two round trips?

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