Some state trooper departments use aircraft to enforce highway speed limits. Suppose that one of the airplanes has a speed of 135 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 70.0 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 135 mi along the highway in 1.00 h. In other words, the ground speed is the same as if there were no wind. (a) From what direction is the wind blowing? (b) What is the heading of the plane; that is, in what direction does it point?

College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Some state trooper departments use aircraft to enforce
highway speed limits. Suppose that one of the airplanes has a speed
of 135 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 70.0 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 135 mi along the highway in 1.00 h. In
other words, the ground speed is the same as if there were no wind.
(a) From what direction is the wind blowing? (b) What is the heading
of the plane; that is, in what direction does it point?

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