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March 25, 2017

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A canoe has a velocity of 0.490 m/s, 45 degrees southeast relative to the earth. The canoe is on a river that is flowing at 0.600 m/s east relative to the earth.

Find the magnitude of the velocity vector v of the canoe relative to the river.
Express your answer in meters per second.

  • Physics - ,

    Draw the triangle of vectors, ABC, where
    AB represents the river velocity, 0.6 m/s due east, BC is the canoe velocity, 0.49 m/s due south-east.
    You are looking for the resultant vector AC.

    You can solve this by the law of cosines, which is
    AC²=AB²+BC²-2AB.BC.cos(135°)

    or by summing components along the x- and y-axes (East and north).
    Resultant:
    x-component=0.6+0.49cos(-45°) m/s
    y-component=0.49sin(-45°) m/s
    tan(θ)=y-component/x-component

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