Answer to Question #236326 in Physics for eshiii

Question

3. A canoe has a velocity of 0.40 m/s southeast relative to the earth. The canoe is on a river that is flowing, 0.50 m/s east, relative to the earth. Find the velocity (magnitude and direction) of a canoe relative to the river.

Answer 1

The velocity (magnitude and direction) of the canoe relative to the river is

$$0.4\cos45°=0.5-v_{crE},\\ v_{crE}=0.5-0.4\cos45°=0.22\text{ m/s}.\\ v_{crS}=0.4\sin45°=0.28\text{ m/s South}.\\\space\\ v_{cr}=\sqrt{v_{crE}^2+v_{crS}^2}=0.36\text{ m/s},\\\space\\ \theta=\arctan\frac{v_{crS}}{v_{crE}}=52°\text{ S of E}$$