SOLUTION: A canoe is paddled at 4km/h directly across a river that flows at 3kh/h. (a) what is the resultant speed of the canoe? (b) How fast and in what direction can the canoe be paddled t

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Question 216635: A canoe is paddled at 4km/h directly across a river that flows at 3kh/h. (a) what is the resultant speed of the canoe? (b) How fast and in what direction can the canoe be paddled to reach a destination directly across the river.
Answer by Alan3354(69443) (Show Source):
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A canoe is paddled at 4km/h directly across a river that flows at 3kh/h. (a) what is the resultant speed of the canoe? (b) How fast and in what direction can the canoe be paddled to reach a destination directly across the river.
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It's sqrt(4^2 + 3^2)
= 5 kph
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(b) How fast and in what direction can the canoe be paddled to reach a destination directly across the river.
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The canoe's heading has to be upstream.
The angle of the heading depends on the speed of the canoe (if the speed of the stream is fixed).
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The sine of the angle of "crabbing" is 3/speed of the canoe.
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If as in the example, the canoe is paddled at 4 kph, then the angle will be
arcsin(3/4) = ~ 48.59 degs
If it's paddled 10 kph, then the angle will be 17.46 degs.