Problem: A canoe has a velocity of 0.400 m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.460 m/s east relative to the earth. (Figure 1) Find the magnitude of the velocity vc/r of the canoe relative to the river.Express your answer in meters per second.

FREE Expert Solution

Vector magnitude,

|v|=vx2+vy2

Resolving vector components,

vx=|v| cos θvy=|v| sin θ

Let positive y-axis point to the north and positive x-axis point to the east. 

Resolving components,

vr/e= 0.460 m/s (cos 0° i + sin 0° j) = 0.460 m/s i + 0 m/s j

vc/e= 0.400 m/s {cos (- 45°) i + sin (- 45°) j } = 0.283 m/s i - 0.283 m/s j

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Problem Details

A canoe has a velocity of 0.400 m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.460 m/s east relative to the earth. (Figure 1) 

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

Express your answer in meters per second.

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Our tutors have indicated that to solve this problem you will need to apply the Relative Motion in 2D concept. You can view video lessons to learn Relative Motion in 2D. Or if you need more Relative Motion in 2D practice, you can also practice Relative Motion in 2D practice problems.