Some state trooper departments use aircraft to enforce highway speed limits. Sup

Question

Some state trooper departments use aircraft to enforce highway speed limits. Suppose one of the airplanes has a speed of 135 mph 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 mph wind is blowing, but neglects the direction. The pilot observes that in spite of the wind, the plane can travel 135 mph. Determine

1. A diagram, depicting this situation

2. The direction the wind is blowing

3. The direction the plane is pointing.

Explanation / Answer

The velocity of the plane with respect to the air is ~vpa; the velocity of the air with
respect to the ground is ~vag, the velocity of the plane with respect to the ground is ~vpg. Then
~vpg = ~vpa + ~vag.

we can find the angle between ~vag and ~vpg (points north) using the cosine law

theta = cos^-1 ( 135)^2 - ( 135)^2 - (70)^2/ - 2 (135) (70))

=75 degree

(b)

The direction of ~vpa can also be found using the cosine law,

theta = cos^-1 ( 70)^2 - (135)^2 - (135)^2/-2(135)(135) ) = 30 degree

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