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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.

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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.

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Thanks. Got the question right. –  a sandwhich Sep 26 '11 at 20:44
    
@a sandwich: If you're a pilot, like me, you get really handy with this stuff. –  Mike Dunlavey Sep 26 '11 at 20:53
    
That is what my teacher said. It makes quite a bit of sense now. –  a sandwhich Sep 27 '11 at 1:07
    
@a sandwich: Use of vectors and basic physics in aviation: wind calculations, turn geometry, angle of attack, weight and balance, crosswind landing, fuel burn, unusual attitudes, climb & descent rates, weight-speed-power-attack angle, ground effect, compass behavior, altitude compensation, potential & kinetic energy management, lift & drag, ... –  Mike Dunlavey Sep 27 '11 at 2:04
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