Dear oriont,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.
Please refer to the attached drawing. Your magnitude of the resultant vector is correct. But b should be 3.69 degrees.