Relative Velocity: Riverboat and Canoe

[Prof. 27]

Homework Statement

A canoe has a velocity of 0.420 m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.550 m/s east relative to the earth.

This can't be seen in the problem statement, but the angle between the two vectors is 45 degrees. As implied by the question, the southeastern one is off at a tilt; while, the river (the eastern one) is at the origin pointing outward straight, horizontally at 0 degrees.

Find the magnitude of the velocity v⃗ c/r of the canoe relative to the river.

Homework Equations

Vsub(B|A) = Vsub(BC) - Vsub(AC)

The Attempt at a Solution

So I thought: Find the magnitude of the tilted vector and then subtract 0.55 from it. This has turned out to be wrong. I did:

Square Root(0.42*Sin(Pi/4)^2 + 0.42Cos(Pi/4)^2) = |Canoe|
|Canoe| - 0.55 = 0.612
Wrong answer

 

[Dr. Courtney]

To add or subtract vectors, it is necessary to compute the x and y components of each vector.

The x component of the sum is the sum of the x components. etc.