How Do You Calculate the Velocity of a Canoe Relative to a River?

[Lemniscate]

Homework Statement

I have to find the magnitude of the velocity of vector Vcanoe/river of a canoe relative to the river.

The canoe has a velocity of 0.520 m/s southeast relative to the earth. The canoe is on the river that is flowing at 0.460 m/s east relative to the earth.

The angle made my both vectors is 45 degrees.


2. The attempt at a solution

I figured the components of the vector Vriver are <0.460,0> m/s
Components of the vector Vcanoe are approximately <0.707,0.707> m/s since we are working with a 45 degree angle.
Are my components correct?

I need subtract both vectors to get the Vcanoe/river.
I got <0.247,0.707> m/s. Yes?

I'm not sure if my components are correct and I'm not sure what to do afterwards.
Any help would be greatly appreciated!

 

[Lemniscate]

Nevermind!
I have found the answer! :D

 

[tomcue]

Based on the given information, it seems like you are on the right track. The components of the vector Vriver are correct, as the river is only flowing in the east direction. However, the components of the vector Vcanoe should be <0.520,0> m/s since it is moving southeast, which means it has a component in both the east and south directions.

To find the magnitude of the velocity of the canoe relative to the river, you will need to use vector addition. This involves adding the components of both vectors together to find the resultant vector. In this case, the resultant vector would be <0.980,0.707> m/s.

To find the magnitude, you can use the Pythagorean theorem, which states that the magnitude of a vector (in this case, the resultant vector) is equal to the square root of the sum of the squares of its components. In this case, the magnitude of the canoe's velocity relative to the river would be approximately 1.193 m/s.

I hope this helps! Remember to always check your units and make sure they are consistent throughout your calculations. Also, be sure to include direction in your final answer, as vectors have both magnitude and direction.