A radar station, located at the origin of xz plane, as shown in the figure (Figu

Question

A radar station, located at the origin of xz plane, as shown in the figure (Figure 1) , detects an airplane coming straight at the station from the east. At first observation (point A), the position of the airplane relative to the origin is R?AR_vec_A. The position vector R?AR_vec_A has a magnitude of 360 m and is located at exactly 40 degrees above the horizon. The airplane is tracked for another 123 degrees in the vertical east-west plane for 5.0 s, until it has passed directly over the station and reached point B. The position of point B relative to the origin is R?BR_vec_B (the magnitude of R?BR_vec_B is 880 m). The contact points are shown in the diagram, where the x axis represents the ground and the positive z direction is upward.

Explanation / Answer

The attempt at a solution

Vector A:

cos 40 = x/360; x = 276

sin 40 degrees = y/360; y = 231

RAx, RAz= (275.775 , 231.40)

Vector B:

angle (123+40=163; 180-163=17 degrees)

cos 17 = x/880; x =-841.55

sin 17 = y/880; y = 257.29

RBx,RBz= (-841.55, 257.29)

RBA = Vector B - Vector A = (-841.55, 257.29) - (275.775 , 231.40) = (-1117.33,25.89)

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