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Plane to Ship Displacement (using component method)

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data
    A coastguard station locates a ship at range 15.4 km and bearing 123° clockwise from north.

    From the same station a plane is at horizontal range 19.4 km, 150° clockwise from north, with elevation 2.06 km.

    What is the vector displacement from plane to ship, let i represent east, j north, and k up.

    2. Relevant equations



    3. The attempt at a solution
    Shipx=15.4cos123 = -8.39i km
    Shipy=15.4sin123 = 12.92j km


    Planex=19.4cos150 = -16.8i km
    Planey=19.4sin150 = 9.7j km
    Planez=2.06 k km

    Therefore Displacement PtoS = (P-S)
    =(-8.41i , -3.22j , 2.06k) km

    Any help you could give me would be greatly appreciated!
     
    Last edited: Sep 27, 2009
  2. jcsd
  3. Sep 27, 2009 #2

    Delphi51

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    You seem to have these reversed; the sine gives the i (east) value.
     
  4. Sep 27, 2009 #3
    Really? So Sin is for the X direction, and cos is for the Y? That's not what my textbook says?
     
    Last edited: Sep 27, 2009
  5. Sep 27, 2009 #4

    Delphi51

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    I hate to make a general statement about this with angles greater than 90 degrees.
    But if you draw the diagram and note that the ship is 57 degrees away from the south line, then you would naturally say that sin(57) = x/15.4 so x = 15.4*sin(57) = 12.9 to the east.
     
  6. Sep 27, 2009 #5

    Yeah I did draw a diagram, I just don't have a scanner to upload it.
    I never thought to look at it as two triangles though.

    So what I actually should have is:

    Shipx=15.4sin57 = 12.9i
    Shipy=15.4cos57 = -8.39j

    Planex=19.4sin30 = 9.7i km
    Planey=19.4cos30 = -16.8j km
    Planez=2.06k km

    Therefore Displacement PtoS = (P-S)
    =(-3.20i , -8.41j , 2.06k) km



    Right??
     
    Last edited: Sep 27, 2009
  7. Sep 27, 2009 #6

    Delphi51

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    Hmm, from the plane you would have to go east, north and down to get to the ship.
    Therefore I think it should be (3.2i, 8.41j, -2.06k).
     
  8. Sep 27, 2009 #7
    Makes sense. Thanks again for the help! :)
     
  9. Sep 27, 2009 #8

    Delphi51

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    Most welcome.
     
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