Dynamics - relative motion, planes Q

[chuffy]

Homework Statement

Aircraft A is describing a circular flight path in an anti-clockwise direction at 125km/h
Aircraft B is flying the same path but in the opposite direction at 225km/h.

If the radius of the flight path is 5km, calculate the acceleration of A relative to B when Aircraft A is heading South-East, with aircraft B is heading South -West

Homework Equations

aA/B = aA - aB

The Attempt at a Solution

Simple looking question but I'm falling at the 1st hurdle with obtaing the angular orientation of each Velocity vector of each Aircraft

My frame of reference is an Oxy diagram

The worked soultion from my tutor is:
θA = 45° when heading south-east
θB = 135 when heading south - west

I don't get the same angles as the worked example & I've doubled checked the directions of the flight paths (A flying anti-clockwise , B flying clockwise)

The only time my angles match the worked soulution is when I make A fly clockwise & B fly antiCan someone check to worked soultion is correct with the question & explain it to me or am I right?

Cheers

 

[PhanthomJay]

The angle depends upon from which axis it is measured and in which direction.
θA = 45° clockwise from the + x-axis when heading south-east
θB = 135 clockwise from the + x-axis when heading south - west

By convention, angles are usually measured ccw from the + x axis, so θA = 315 degrees counterclockwise from the + x-axis when heading south-east
θB = 225 counterclockwise from the + x-axis when heading south - west

In reality, a pilot measures his or her bearing clockwise from magnetic north, so SE is 135 degrees and SW is 225 degrees.

In the end, the relative accelerations come out the same no matter how you choose your angles, as long as you are consistent..

 

[chuffy]

Thanks for the detailed reply

The 1st part of your answer matches my thinking that θA is° flying clockwise
However, the question states anti-clockwise

However, I tried your method of being consistent with measuring the angles from the x-axis & going counter clockwise to get a positive angle & it worked.

I think the circluar flight paths were throwing me off as on one question it stated:

Aircraft A flys counter clockwise & is heading south. I thought the angle would be 180° but I now understand why it is actually 270°