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Vector airplane distance problem

  1. Sep 1, 2012 #1
    1. The problem statement, all variables and given/known data

    An air-traffic controller observes two aircraft on his radar screen. The first is at altitude 900 m, horizontal distance 19.0 km, and 25.0° south of west. The second aircraft is at altitude 1200 m, horizontal distance 17.6 km, and 17.0° south of west. What is the distance between the two aircraft? (Place the x axis west, the y axis south, and the z axis vertical.)


    2. Relevant equations



    3. The attempt at a solution

    my vectors for each airplane are:

    <17.22, 8.03, .9>
    <16.83, 13.18, 2.1>

    adding them together and then getting the resultant i get 36.57 kilometers, however thats wrong and i'm not sure what i did wrong.
     
  2. jcsd
  3. Sep 1, 2012 #2

    cepheid

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    For your second vector, neither the y-component nor the z-component is correct.
     
  4. Sep 1, 2012 #3

    cepheid

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    Also, adding them together and taking the resultant is not what you want to do. Think about it. Draw a picture.
     
  5. Sep 1, 2012 #4
    sorry that was a typo...i accidently wrote down the added values.

    ahh i see, i believe i should have subtracted the vectors?
     
  6. Sep 1, 2012 #5
    reworking the problem by subtracting, i get 2.96 km...could someone verify my answer?
     
  7. Sep 1, 2012 #6

    cepheid

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    Subtracting is the right thing to do to find a vector that goes from one plane to the other. Then you need to find the magnitude of this vector.

    I get an answer that is pretty close to that.
     
  8. Sep 1, 2012 #7
    ok yes that is what i did for my second answer...thank you for the help!
     
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