A canoe has a velocity of 0.380 m/s southeast relative to the earth. The canoe i

Question

A canoe has a velocity of 0.380 m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.560 m/s east relative to the earth. (Figure 1)

Part A

Find the magnitude of the velocity v c/r of the canoe relative to the river.

Express your answer in meters per second.

Hints

A canoe has a velocity of 0.380 m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.560 m/s east relative to the earth. (Figure 1)

Part A

Find the magnitude of the velocity v c/r of the canoe relative to the river.

Express your answer in meters per second.

Hints

Explanation / Answer

Here the velocity of the canoe relative to the river is equal to the velocity of the canoe minus the velocity of the river, using vector addition/subtraction...

i^ = the unit vector in the x-direction, setting east as positive

j^ = the unit vector in the y-direction, setting north as positive

Vc = 0.38cos(45°) i^ + -0.38sin(45°) j^

Vr = 0.56 i^

Vc/r = Vc - Vr = [0.38cos(45°) - 0.56] i^ + [-0.38sin(45°) - 0] j^

Vc/r = -0.291 i^ -0.2687 j^

Magnitude Vc/r = ((-0.291)² + (-0.2687)²) = 0.396 m/s

Angle = arctan (-0.2687 / -0.291) = 42.718° south of west

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