Dolly Robinson

2021-01-13

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 $\overrightarrow{{R}_{A}}$. The position vector $\overrightarrow{{R}_{A}}$ has a magnitude of $360}^{m$ and is located at exactly $40}^{\circ$ above the horizon. The airplane is tracked for another $123}^{\circ$} 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 $\overrightarrow{{R}_{B}}$ (the magnitude of $\overrightarrow{{R}_{B}}$ 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: ${\overrightarrow{R}}_{BA}={\overrightarrow{R}}_{B}-{\overrightarrow{R}}_{A}$. What are the components of ${\overrightarrow{R}}_{BA}$

Express ${\overrightarrow{R}}_{BA}$ in meters as an ordered pair, separating the x and z components with a comma, to two significant figures.

sovienesY

Skilled2021-01-14Added 89 answers

The position vector

Substitute (360m) for r and 40 deegres for

The position vector

The angle for the position vector

Substitute (880m) for r and 163 deegres for

The resultant displacement vectors components of the air plane are,

Substitute

Therefore, the displacement of the airplane as an ordered pair separated by the x and z components is (-1100m,26m).

Jeffrey Jordon

Expert2021-09-30Added 2605 answers

Vector A:

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