In the figure, a radar station detects an airplane approaching directly from the

Question

In the figure, a radar station detects an airplane approaching directly from the east. At first observation, the airplane is at distance d1 = 320 m from the station and at angle theta 1 = 38 degree above the horizon. The airplane is tracked through an angular change Delta theta = 115 degree in the vertical east-west plane; its distance is then d2 = 820 m. Find the magnitude and direction of the airplane's displacement during this period. Give the direction as an angle relative to due west, with a positive angle being above the horizon and a negative angle being below the horizon.

Explanation / Answer

d1 = 320 @ 38

Hence

D1 = 320 Cos38i + 320sin38j

D2 = 820cos 153i + 820sin153 j

Displacement = D2 - D1 = (820cos 153 - 320 Cos38)i + ( 820sin153 - 320sin38)j

= -982.79 i + 175.26 j

= 998.295 m

Angle = arcstan(175/26/-982.79)

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