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.
2 answers
It is not clear from the question what the "true" velocity means, and what the direction of the runway is. If it is the air speed, then there must be a tail wind, not a head wind. This is a vector addition question, but I hesitate to try to solve it because I might be solving the wrong problem.
oh, okay, well, thanks for trying; I wish I could givr you more information, but that's all my worksheet says...