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 = 360 m from the station and at angle 1 = 39° above the horizon. The airplane is tracked through an angular change = 127° in the vertical east–west plane; its distance is then d2 = 810 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.

Explanation / Answer

from the given data, we have
x = 360m * cos39º = 269.77 m
and y = 360m * sin39º = 226.55 m

the angle above the horizon is calculated as  
= 180º - 127º - 39º = 14º

hence, we have

x' = 810m * cos14º = 785.94 m
and y' = 810m * sin14º = 195.96 m

so the magnitude of displacement is
d = sqrt[(785.94+269.77)2 +(226.55 + 195.96)2] = sqrt[(1055.71)2 +(422.51)2]

d = 1137.12 m

the direction is
=arctan(422.51/1055.71) = 21.8º = 22º west

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