A radar station, located at the origin of xz plane, as shown in the figure , detects an airplane coming straight at the station from the east.

Dolly Robinson 2021-01-13 Answered

A radar station, located at the origin of xz plane, as shown in the figure , 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 RA. The position vector RA has a magnitude of 360m and is located at exactly 40 above the horizon. The airplane is tracked for another 123} in the vertical east-west plane for 5.0s, until it has passed directly over the station and reached point B. The position of point B relative to the origin is RB (the magnitude of RB is 880m). The contact points are shown in the diagram, where the x axis represents the ground and the positive z direction is upward.
image
Define the displacement of the airplane while the radar was tracking it: RBA=RBRA. What are the components of RBA
Express RBA in meters as an ordered pair, separating the x and z components with a comma, to two significant figures.

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Expert Answer

sovienesY
Answered 2021-01-14 Author has 89 answers

The position vector RA is given by
RA=(rcosθ)i^+(rsinθ)k^
Substitute (360m) for r and 40 deegres for θ to find RA
RA=((360m)cos40)i^+((360m)sin40)k^
=(275.8m)i^+(231.4m)k^
The position vector RB is given by,
RB=(rcosθ)i^+(rsinθ)k^
The angle for the position vector over{R}B along vertical and horizontal plane is,
θ=123+40=163
Substitute (880m) for r and 163 deegres for θ to find RB
RB=((880m)cos163)i^+((880m)sin163)k^
=(841.5m)i^+(257.3m)k^
The resultant displacement vectors components of the air plane are, RBA=RBRA
Substitute (841.5m)i^+(257.3m)k^ for RB and (275.8m)i^+(231.4m)k^ for RA to find RBA.
RBA=(841.5m)i^+(257.3m)k^(275.8m)i^+(231.4m)k^
=(1117.3m)i^+(25.9m)k^ Round off the components of resultant displacement vectors in to two significant figures, RBA=(1100m)i^+(26m)k^
Therefore, the displacement of the airplane as an ordered pair separated by the x and z components is (-1100m,26m).

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Jeffrey Jordon
Answered 2021-09-30 Author has 2047 answers

Vector A:

cos40=x360; x = 276

sin40=y360; y = 231

RAx,RAz=(275.775,231.40)

Vector B:

(123+40=163;180163=17)

cos17=x880;  x=841.55

sin17=y880;  y=257.29

RBx,RBz=(841.55,257.29)

RBA=BA=(841.55,257.29)(275.775,231.40)=(116.84,25.89)
 

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