Question

A pilot maintains an airspeed of 175mph and a heading of 45.0 degrees and encounters a wind with velocity 25 mph@270.0 degrees. Determine the aircraft’s velocity relative to the earth

Answer 1

Let me first draw a quick diagram of the vectors so you can understand what you need to do



See it now? That's right, you need to add vectors to find the resultant. And since it is asking for velocity, you must be sure to find the final direction, along with the magnitude.

1. Find the vector components for each vector. Here, since your directions are straightforward, you might as well use special right triangles.
2. Add each component
3. To find the new direction, take the tan inverse of the two components. To find the magnitude apply the pythagorean theorem.