A radar station, located at the origin of xz plane, as shown in the figure (Figu
ID: 584350 • Letter: A
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 A. The position vector R 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 B (the magnitude of R 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.
Define the displacement of the airplane while the radar was tracking it: R BA=R BR A. What are the components of R BA?
Express R BA in meters as an ordered pair, separating the x and z components with a comma, to two significant figures.
Explanation / Answer
Given are
Ra=360m at 40 degrees
Rb=880m at (123+40)=163 degrees
T=5sec
X component of Ra
=360 cos 40
=275.7 m
Y component of Ra
=360sin 40
=231.4m
X component of Rb
=880 cos 163
=-841.5 m
Y component of Rb
=880sin 163
=257.2 m
Xcomponent
R=275.7-(-841.5)
=1117.2
Y component
R=231.4-257.2
=-25.8 m
Rb-Ra=undrt(1117.2^2+25.8^2)
=1117.4 m--answer