I have done this question repeatedly and arrived at the same result, but webassign won't accept my answer.
Please DO NOT post the steps to the solution in your answer or give it away to me.
The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45°W at a speed of 40 km/h. (This means that the direction from which the wind blows is 45° west of the northerly direction.) A pilot is steering a plane in the direction N60°E at an airspeed (speed in still air) of 300 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find the true course and the ground speed of the plane. (Round your answers to one decimal place.)
After getting $\mathbf{w} = \langle -28.2843, 28.2843 \rangle$ and $\mathbf{p} = \langle 259.8076, 150 \rangle$, I got $\mathbf{p} + \mathbf{w} = \langle 231.5233, 178.2843 \rangle$.
Then I just found $|r|$
My answer: 292.2 km/h and 52.4 degrees East of North. How could that be wrong?
Can you confirm that this answer is correct so I can tell the prof, or have I messed up?
Best Answer
I just did the vector addition and got a different answer to you, both in terms of the magnitude of the vector and the angle.
I can see where you went wrong, however you specifically said "Please DO NOT post the steps to the solution in your answer or give it away to me." As I am unsure of how much help you want, I am posting the bare minimum. If you want any further details, please tell me.