Velocity of canoe relative to river physics?

Question

A canoe has a velocity of 0.310 southeast relative to the earth. The canoe is on a river that is flowing at 0.560 east relative to the earth. Find the magnitude of the velocity of the canoe relative to the river.

Answer 1

The velocity vector of the canoe relative to the river is found by subtracting the velocity vector of the river from the velocity vector of the canoe. If you draw these three vectors as a triange, you'll see that the angle between the two known vectors is 45 degrees, and therefore we have enough to find the length of the unknown vector by using the law of cosines. The magnitude of the canoe relative to the river is sqrt(0.31^2 + 0.56^2 - 2*0.31*0.56*cos(45)) = 0.405.

Answer 2

Canoe On A River