In some basic physics homework I have, it asks what the resulting vector would be for a plane traveling at x m/s in y direction that is affected by a tailwind going in z direction at w m/s. How would I calculate this? I know basic vector addition, but this has stumped me.
First rename your variables to something other than x, y, and z, because you're going to need x and y as coordinates.
Let V be the aircraft's velocity vector relative to the air. It has a direction and length.
Let W be the wind vector relative to the ground. It has a direction and length.
Add vectors V+W, and you get G, the velocity vector of the aircraft with respect to the ground.