You are flying in a single engine plane from New Orleans to Houston for an important meeting. From New Orleans, you head due west towards Houston, which is $315$ miles away, but shortly after takeoff your plane’s navigational equipment goes out. You press on and, as you reach the cruising altitude of $14{,}000$ feet, you encounter a headwind blowing towards the southeast at $64$ mph. The plane’s cruising speed is $210$ mph, but the wind will affect the plane’s speed and direction. What are the true speed and heading of the plane?

1. Draw and label a vector diagram for this situation. In particular, find and label the angle between the plane’s velocity vector and the wind velocity vector.

   Answer (a):

   

2. Add a vector representing the resulting velocity vector for the plane.

   Answer (b):

   

3. Find the plane’s true speed and bearing.

   Answer (c):

   $170.848$ mph, $254.6º$