A canoe has a velocity of 0.330 m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.540 m/s east relative to the earth. Find the velocity (magnitude and direction) of the canoe relative to the river.

The velocity of the canoe relative to the river is 0.385 m/s, S37.26⁰W

Explanation:

Given;

velocity of the canoe relative to the earth,

velocity of the river relative to the earth,

The velocity of the canoe relative to the river is calculated as;

The x - component of the velocity of the canoe relative to the earth;

The y-component of the velocity of the canoe relative to the earth;

Note: velocity of the river relative to the earth has only x-component = 0.54 m/s

Apply equation (1) and (2) to calculate the velocity of the canoe relative to the river;

answer: 31, 5556. 952 seconds