A canoe has a velocity of 0.55 m/s southeast relative to the earth. The canoe is

Question

A canoe has a velocity of 0.55 m/s southeast relative to the earth. The canoe is on a river that is flowing 0.52 m/s east relative to the earth.

A - Find the magnitude of the velocity of the canoe relative to the river.

B - find the direction of the velocity of the canoe relative to the river.

(I looked at the other similar questions and can't seem to get the right numbers. I'm missing something important here. Is my angle 45 or 135 or 315? I've seen answers with 3 different numbers. Thank you.)

Explanation / Answer

a) Suppose x axis is towards the right and y axis is towards the up.
Velocity of canoe v_c= 0.55(cos(45) i^ - sin(45) j^) m/s

Velocity of the river v_r = 0.52 i^ m/s

velocity of canoe relative to the river v_cr = v_c-v_r = -0.13 i^ - 0.39 j^ m/s

magnitude = 0.41 m/s

b) angle = 71.56 degree south of west.

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