Given:

• The plane is flying due West the entire trip.
• The plane's engines put out enough power to fly at 545 mph if there is no wind (but they could put out more if needed).

When the plane crosses over Detroit, the wind speed at flight altitude is 45 mph @ 45 degrees South of East. If the plane does not make any corrective action, the wind will both slow it down and knock it off course. How can I calculate the new velocity vector (both magnitude and direction) for the plane? Please show how I suppose to solve a problem like this, how can I set up aa diagram and algebraic solution?