Question

Define the displacement of the airplane while the radar was tracking it: r⃗ ba=r⃗ b−r⃗ a. What are the components of r⃗ ba? express r⃗ ba in terms of the unit vectors i^ and j^, in meters.

Answer 1

The given magnitude and direction of $\vec {R}_A$ and $\vec R_B$, can be

expressed in terms of unit vectors, to give $\vec R_A$ - $\vec R_B$.

Correct response:

• The component form of $\vec R_{BA}$ is $\underline{-1117.47 \cdot \mathbf{\hat i} - 18.49 \cdot \mathbf{\hat j}}$

• The magnitude of $\vec R_{BA}$ is 1117.47 meters

Which is the method used to find the displacement vector?

The possible parameters obtained from a similar question posted online are;

Magnitude of $\vec R_{A}$ = 360 m

Direction of $\vec R_A$ = 40° above the horizon

Magnitude of $\vec R_B$ = 880 m

Direction of $\vec R_B$ = Another 123° from $\vec R_A$

Required:

The displacement of the airplane, while the radar was tracking it, $\vec R_{BA}$ = $\vec R_B$ - $\vec R_A$

Solution;

$\vec R_A$ = 360 × cos(40°)·$\mathbf{ \hat i}$ + 360 × sin(40°)·$\mathbf{\hat j}$

$\vec R_B$ = 880 × cos(123° + 40°)·$\mathbf{\hat i}$ + 880 × sin(123° + 40°)·$\mathbf{ \hat j}$

Which gives;

$\vec R_{AB}$ = (880 × cos(163°) - 360 × cos(40°))·$\mathbf{\hat i}$ + ((880 × sin(163°) - 360 × cos(40°))·$\mathbf{\hat j}$

Which gives;

• $\vec R_{AB}$ = -1117.32·$\mathbf{\hat i}$ - 18.49·$\mathbf{\hat j}$

Therefore;

• In terms of unit vectors is, $\hat R_{BA}$ = $\underline{-1117.32 \cdot \mathbf{\hat i} - 18.49 \cdot \mathbf{\hat j}}$

The magnitude of $\vec R_{AB}$ ≈ √((-1117.32)² + (-18.49)²) ≈ 1117.47

• Which gives the magnitude of the displacement, of the airplane is approximately 1117.47 meters

Learn more about vectors here:

https://brainly.com/question/24855749