A plane tries to head away from an airport at 500km/h[N], but finds that its true velocity is 450km/h[N35degreesE] due to headwinds. What is the velocity of the wind?
I'm supposed to be using components, so for N-S I used 500+450sin(55 which got me 868.6 then, for E-W I did 450cos(55 and that was 258.1. I then used pythagorean theorem and square rooted 868.6^2+258.1^2 and that was 906 km/h.
Then, I did the inverse tan of 25831/868.6 and got 16.5 as the angle. Howeverm this would mean that the wind's velocity is 906 km/h[N16.5degreesE], but this is a headwind, and I think it should be coming in an oppoisng direction, right? I'm just really confused and don't really know what to do. Please, please help me understand this.
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