This is my homework problem:

Question

"The pilot of a plane is flying at 450 mi/hr W 20.0 degrees S relative to the earth. She sees another plane flying at 350 mi/hr N 40.0 degrees W relative to her plane. What was the magnitude and direction of the plane she saw relative to the earth?"

I'm not entirely sure where to start because relative motion is something I'm still trying to grasp. What do I start with to find the magnitude?

Answer 1

Velocity of the other plane with respect to Earth =
Velocity of the other plane w.r.t. her plane
+ Velocity of her plane w.r.t. Earth

Perform the vector addition

Answer 2

That doesn't require me to find the x and y components of those vectors, does it?

Answer 3

Yes it does. It's not hard.
Call North the +y direction and east the +x direction.

It is not clear to me if "W 20.0 degrees S" means "20 degrees west of south" or "20 degrees south of west". You will need to clarify the terminology to answer the question.

Answer 4

So, would the components look something like this:
450cos200
450sin200

350cos130
350sin130