How Should Direction Be Adjusted in Relative Velocity Problems?

[Jacobpm64]

I have a couple of problems.. I'll show all my work...

A swimmer wants to swim due east in a stream that flows due south. In which direction should the swimmer swim?
The choices are east, north, northeast, south, southeast, and west... I chose Northeast.


Here's another question... use the bolded situation for the next 2 questions.

A plane flies west with a 100km/h velocity with respect to the air while the wind is blowing toward the north at 65km/h relative to the ground.

If the plane wants to fly directly west with respect to the ground, in what direction should he head his plane with respect to the air?
southwest? I'm not sure.. i think i need degrees for this too...

What if the wind is blowing directly south rather than north, where should the pilot head his plane if he wants to go directly west?
northwest? I'm not sure.. i think i need degrees for this too...

 

[Claude Bile]

Relative velocity problems are simple vector subtractions.

Diagramatically, you can represent the velocity of an object with a vector. The length of the vector represents the magnitude of the velocity, while the direction of the vector is simply the direction the object is travelling.

When adding vectors, simply place the vectors head to tail. The sum is the vector that joins the free 'tail' to the free 'head' (in that order, so the 'head' of the sum vector corresponds to the free head in the diagram). To subtract vectors, simply add a vector that is equal in magnitude but opposite in direction.

When you complete these subtractions, you get a triangle. From there it is a matter of using trigonometry to figure out magnitudes and directions.

Claude.