Just wanted to have someone check the answer I got to this problem, since its not in the back of the book.
The problem reads: An airplane is heading northeast at an airspeed of 700km/hr, but there is a wind blowing from the west at 60km/hr. In what direction does the plane end up flying? What is its speed relative tot he ground?
[Hint: Resolve the velocity of the vectors for the airplane and the wind into components] This hint portion confuses me, and not quite certain how to do what they asked, I went a different route.
Since the wind is coming west at 60 with a 45° angle between the wind and the northeast direction of the plane at 700, I use the law of cosine to get A (side joining the tails of 60 and 700 vector) with A^2= 60^2+700^2-2(60)(700)Cos 45°
This comes out to be 658.94, which I think is the speed of the plane.
To get the direction of I used the law of sines and came up with sin45°/658.94 = sinb/60 (b=angle between vector 700 and the vector that joins the vectors 700 and 60. This comes out to be 4.079, which I think is the angle east of north that the plane is traveling.
Not too sure of this, so thanks in advance.