Posted by Anonymous on .
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 
MathMate,
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 southeast.
You are looking for the resultant vector AC.
You can solve this by the law of cosines, which is
AC²=AB²+BC²2AB.BC.cos(135°)
or by summing components along the x and yaxes (East and north).
Resultant:
xcomponent=0.6+0.49cos(45°) m/s
ycomponent=0.49sin(45°) m/s
tan(θ)=ycomponent/xcomponent