# Relative velocity of a canoe problem

1. Oct 8, 2011

1. The problem statement, all variables and given/known data

A canoe has a velocity of 0.470m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.490 m/s east relative to the earth.Find the magnitude of the velocity Vc/r of the canoe relative to the river. there is a graph: Vr/e pointed directly on the x axis to the right (positive) and Vc/e pointed 45 degrees down between x positive and y negative axis.

2. Relevant equations

3. The attempt at a solution
I found the east component first;
V=V0*cos 45=0.47*cos45=0.332m/s
V cr=V-Vcriver=0.332m/s-0.490m/s=-0.158 since we need magnitude it's 0.158, however the answer is wrong. Could you please point out my mistakes? Thank you!

2. Oct 10, 2011

### Spinnor

You can make a guess to get things started. If the river runs to the east at .5 m/s and you paddle your canoe to the south at .5 m/s you will end traveling south east at √2 * .5 m/s

We have the right direction but we are moving faster then stated in the problem. What you need is

.47 i + x i = .49 * cos45 i

0 j + y j = -.49 * cos45 j

Solve for x and y. They will be the components of the velocity relative to the river.