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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, there 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?

Thank you very much!

P.K.
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drokkin
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2 Answers2

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Your solution for problem a) is correct.

For the second half of your question, you should obviously paddle with the same speed against the water's flowing direction as the water flows itself. Of course, you keep paddling perpendicular to the shore at 4 km/h.

ConfusedProgrammer
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For the second half of the question consider that the proportion of your movement that coincidences with the movement of the river should be of the same magnitude.

Since you're directly crossing the river your movement and the river's movement meet at a 90° angle, thus your drive against the river is

$$\cos (90°) \cdot 4.0 \text{km/h} - 3 \text{km/h} = 0 \cdot 4.0 \text{km/h} - 3 \text{km/h} = -3 \text{km/h},$$ so you're basically tring to solve

$$v \cdot 4.0\text{km/h} = 3\text{km/h}$$

In order to reach a destination directly across the river you have to adjust the angle $x$ so that it evens out:

$$\cos (x) = \frac{3}{4}$$

Zeta
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