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Dynamics - relative motion, planes Q

  1. Jul 16, 2013 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations

    aA/B = aA - aB

    3. 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 anti

    Can someone check to worked soultion is correct with the question & explain it to me or am I right?

  2. jcsd
  3. Jul 16, 2013 #2


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    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..
  4. Jul 17, 2013 #3
    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°
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