Question

The New Hampshire State Police use aircraft to enforce highway speed limits. Suppose that one of the airplanes has a speed of 130 mi/h in still air. It is flying straight north so that it is at all times directly above a north–south highway. A ground observer tells the pilot by radio that a 60.0 mi/h wind is blowing but neglects to give the wind direction. The pilot observes that in spite of the wind the plane can travel 130 mi along the highway in 1.00 h. In other words, the ground speed is the same as if there were no wind. Assume that the plane is heading a bit west of north. (a) Toward what direction is the wind blowing? (b) What is the heading of the plane; that is, in what direction does it point? Give your directions as angles relative to north, where a positive angle is west of north and a negative angle is east of north.