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 d_1 = 380 m from the station and at angle theta_1 = 32 degree above the horizon. The airplane is tracked through an angular change Delta theta = 116 degree in the vertical east-west plane: its distance is then d_2 = 830 m. Find the (a) magnitude and (b) 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. (a) Number Units m b) Number Units degree(degrees)

Explanation / Answer

Initial position vector = 380(cos32oE + sin32oN)

Angle of final position vector with respect to West direction = 180o - 116o - 32o = 32o

Final position vector = 830(-cos32oE + sin32oN)

Displacement vector, d = 830(-cos32oE + sin32oN) - 380(cos32oE + sin32oN)

=> d = -(830cos32o + 380cos32o)E + (830sin32o - 380sin32o)N = -1026.1E + 238.5N

(a) Magnitude of displacement = [(-1026.1)2 + 238.52]1/2 = 1053.5 m

(b) Direction = tan-1(238.5 / 1026.1) = 13.1o (north of west)

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