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

Question

n 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

Initial height of the plane = d1*sin(theta 1)

=360*sin(39)

=226.55 m

Final angle which the plane make with the negative x axis = 180-39-127

=14 degrees

so height of the plane = d2*sin(14)

=810*sin(14)

=195.95 m

so effective displacement in the horizontal direction = d1*cos(39) + d2*cos(14)

=1065.71 m

Effective displacement in the vertical direction = Final height - initial height

=195.95 - 226.55

=-30.6 m

a) so magnitude of the displacement = (30.6^2 + 1065.71^2)^0.5

=1066.15 m

b)angle = arctan(-30.6/1065.71)

=-1.644 degrees

Hence the angle is 1.644 degrees below the horizon.

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