What is the relative velocity of a canoe on a river?

[bichz33]

A canoe has a velocity of 0.490 m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.510 m/s east relative to the earth.

a)Find the magnitude of the velocity of the canoe relative to the river.

b)Find the direction of the velocity of the canoe relative to the river.

a) Okay for this i used $$\vec{V}_\textrm{(boat/earth)} = \vec{V}_\textrm{(boat/river)} + \vec{V}_\textrm{(river/earth)}$$ and then subtract the Velocities of the boat and river relative to the Earth to equal the velocity of the boat relative to the river so i just used the formula sqrt(A^2+B^2-2ABcos(45)) and got .383 which is the right answer but is there another way to get that answer.

b) and for b i have no clue how to get this...

 

[andrevdh]

Think of the resulting motion (velocity) of the canoe as being produced by that of the river and of that of in which direction the rower is rowing it. These three velocity vectors form a triangle, that is the vector sum of the last two mentioned gives the resultant velocity vector.

 

[bichz33]

Thanks I got it