vectors: finding the actual speed and direction of aircraft

[Spellbinder2050]

My book states the following:

A Boeing 737 aircraft maintains a constant airspeed of 500 miles per hour headed due south. The jet stream is 80 miles per hour in the northeasterly direction.

Express the velocity v of the 737 relative to the air.

Answer: The velocity of the 737 relative to the air is v = -500j
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I'm confused about this answer. If we want to calculated the speed of the plane relative to the air, wouldn't that mean relative to the wind traveling northeast at 80mph? In which case, we would have to figure out how fast the plane is going south with the wind traveling northeast (the wind would be hitting the plane at a 45 degree angle). We would also have to figure out how much the wind is slowing the plane down.

At least this is how I interpret "relative to the air" as. What am I missing? Could someone explain this relativity to me?

[jg.allinsymbols]

"Velocity relative to the air," is not too comfortable wording. Maybe this is just difficult to interpret.

The way I can make sense of the description and question is, the jet is 500 m/h pointing downward (south), the wind vector80 m/h, is 135 degrees to the left relative to the jet's direction; and so you have vector addition of these two vectors. Law of cosines may work well. Other analyses?

[Spellbinder2050]

I had someone give me the following source:

http://en.wikipedia.org/wiki/Airspeed

It didn't really help me much though.

I see that it said that true airspeed is the speed of the plane relative to the atmosphere. However, if you pick a stationary point of space in the atmosphere, it would seem to be the same as airspeed relative to the ground because both the ground and the atmosphere are fixed points.

I'm really annoyed by this already and want to understand what "relative to the air" indicates and why the speed of the plane is not effected by either the wind speed (which I assumed was the air) or the stationary point in the atmosphere (which appears to be the same as relative to the ground).

[jg.allinsymbols]

The intended interpretation must be, what is the velocity of the aircraft in the air ignoring the velocity of the air; just as if the air were not moving relative to the ground.