Track Plane: Find $\hat R_{BA}$ (2 SF)

[EaGlE]

Intro: A radar station detects an airplane coming straight at the station from the east. At first observation (point A), the range to the plane is 360 m at 40 degrees above the horizon. The plane 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 reaches point B. The range at final contact is 880 m. The contact points are shown in the diagram.

Question: What is $$\hat R_{BA}$$ the change of the displacement vector of the plane while the radar was tracking it?

Here, $$\hat R_{BA} = \hat R_{B} - \hat R_{A}.$$ Express $$\hat R_{BA}$$ numerically as an ordered pair, separating the x and z components with a comma, to an accuracy of two significant figures.


my work is also included(work i did is in red)... did i do my calculations correctly?

 

[suffian]

everything looks good except you didn't quite answer the question! the answer should be in the form r = <dx, dy>.

 

[M98Ranger]

Yes, your calculations appear to be correct. The change in the displacement vector, \hat R_{BA}, can be calculated by subtracting the initial displacement vector at point A from the final displacement vector at point B. This can be done by breaking down the displacement vectors into their x and z components and then subtracting them.

At point A, the displacement vector can be represented as (360cos(40), 360sin(40)) = (274.7, 231.5). Similarly, at point B, the displacement vector can be represented as (0, 880) = (0, 880).

Subtracting the x components, we get 0 - 274.7 = -274.7 and subtracting the z components, we get 880 - 231.5 = 648.5.

Therefore, the change in displacement vector, \hat R_{BA}, is (-274.7, 648.5) to two significant figures. This can also be represented as an ordered pair as (-270, 650).

So, the answer to the question would be:

\hat R_{BA} = (-270, 650)