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A canoe has a velocity of 0.490 southeast relative to the earth. The canoe is on a river that is flowing at 0.520 east relative to the earth creating a 45 degree angel between the two velocities.Find the magnitude of the velocity of the canoe relative to the river.

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    Perform the vector operation:

    Vce = Vwe + Vcw where

    Vce = velocity of cane with respaect to earth

    Vwe = velocity of water (river) with respect to earth

    Vcw = velocity of canoe with respect to water. (You want to know its magnitude)

    You have not provided units for your velocity numbers, so that is as far as I can go with this one.

    Vce is at a 45 degree angle to Vwe.

    There are two unknowns: the magnitude of Vcw and its direction. The vector equation will provide the two equations needed (one for east-west and one for north-south components)

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