So here's the problem: Suppose a bird is flying NE at 5m/s into a headwind blowing at 2m/s 30° SE. Find the NE direction in which the bird was flying and it's resulting speed in the east direction.
What I basically have set up so far looks like this (I tried to make it look as clear as possible but i'm not an artist lol):
I know that I'm trying to find for the angle $\theta$ and also the magnitude of the vector (b+w) which I assume is going to be the resulting speed of the bird. Unfortunately, I'm having a lot of difficulty understanding the wording of the problem so I have no idea if what I have set up is even close to right and, even if it is, I have no idea what my next step should be.
I'd really appreciate any help :)
The basic equation is ground speed =air speed + wind speed. You are given the ground speed of the bird. Is the NE in the problem $45^\circ$? I don't see any other way to interpret it. Then just subtract the wind speed to get the air speed. You can split both vectors into N/S and E components and do your arithmetic.