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I'm a bit stuck on a homework question that I've been assigned. The question is as follows:

You are paddling a canoe at a speed of 4 km/h directly across a river that flows at 3 km/h. (a) What is your resultant speed relative to the shore? (b) In approximately what direction should you paddle the canoe so that it reaches a destination directly across the river?

Below the question is a little diagram of a canoe in a river, perpendicular to the shore, with an arrow pointing to the right, labelled 4 km/h, and an arrow pointed downwards, labelled 3 km/h.

I understand the first bit of the question, and have established that the resultant speed relative to the shore will be 5 km/h. Can you please help me with the second half?

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Ask yourself the following

  1. What should the resultant vector be?
  2. Which vector can you influence to change the resultant vector?
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If you are paddling at some angle to the bank, you can resolve your velocity into a component parallel to the bank and a component at right angles to the bank. Your net velocity along the river (i.e. parallel to the bank) is the sum of the river velocity and the component of your velocity parallel to the bank. You need to work out the angle that makes this net velocity zero.

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