# A canoe has a velocity of 0.470m/s southeast relative to the earth.  The canoe is on a river that is flowing at 0.590 m/s east relative to the earth. Find the magnitude of the velocity Vc/r of...

A canoe has a velocity of 0.470m/s southeast relative to the earth.  The canoe is on a river that is flowing at 0.590 m/s east relative to the earth. Find the magnitude of the velocity Vc/r of the canoe relative to the river.

justaguide | College Teacher | (Level 2) Distinguished Educator

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The velocity of the canoe is 0.470 m/s south-east relative to the Earth. It is moving on a river that is flowing at 0.59 m/s towards the East.

The velocity of the canoe with respect to the Earth can be divided into a component towards the East equal to 0.47*sin 45 and a component towards the South equal to 0.47*cos 45. The velocity of the flow of the river is 0.59 m/s towards the East.

Relative to the river, the component of the velocity of the canoe towards the East is 0.47*cos 45 - 0.59 = -0.2576. This implies that the canoe is moving towards the West relative to the river at 0.2576 m/s. It also has a component towards the South equal to 0.3323 m/s.

The magnitude of the velocity of the canoe relative to the river is sqrt(0.2576^2 + 0.3323^2) = 0.4205 m/s

The required magnitude of the velocity Vc/r = 0.4205 m/s.