Really getting started precal, physics problem

[bennett]

an airplane's velocity with respect to the air is 400 kilometers per hour, with a bearing of 45degrees. The wind at the altitude of the plane has a velocity of 40 kilometers per hour with a bearing of N50degeeesE. What is its speed relative to the ground

Ok I am not asking you to do the problem for me i just don't have all my notes on me and the book isn't much help I would really appreciate it if someone could help me get started on this problem, thanks.

 

[Astronuc]

Add the plane's velocity (a vector) to the air's velocity (another vector) to get the plane's velocity (the resultant vector).

One has to pick a coordinate system, e.g. N (+y), E (+x), S (-y), W (-x), and be consistent.

N50E means 50 degrees toward the east from N.

One has to resolve the velocity vector into two normal components (x, y) and add or subtract corresponding x and y components of the two vectors.

 

[einstein2]

"an airplane's velocity with respect to the air is 400 kilometers per hour, with a bearing of 45degrees." Does this mean with respect to the air's velocity? I.e. is the bearing of the plane 45 degrees clockwise from the bearing of the air?

 

[Astronuc]

"an airplane's velocity with respect to the air is 400 kilometers per hour, with a bearing of 45degrees." Does this mean with respect to the air's velocity? I.e. is the bearing of the plane 45 degrees clockwise from the bearing of the air?

The magnitude of the velocity (speed) is with respect to the air, the orientation is with respect to the coordinate system, which is irrespective (independent) of the media (air) in which the airplane is traveling.