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Vector component addition

  1. Sep 16, 2011 #1
    Two geological field teams are working in a remote area. A global positioning system (GPS) tracker at their base camp shows the location of the first team as 38 km away, 19° north of west, and the second team as 29 km away, 35° east of north. When the first team uses its GPS to check the position of the second team, what does the GPS give for the distance between the teams and direction,θ, measured from due east?

    2. Relevant equations
    Fx = Fax + Fbx
    Fy = Fay + Fby

    Resultant vector = sqrt[ (Fx2 + Fy2 ]

    Θ = tan-1 (Fy/Fx)

    3. The attempt at a solution
    Fx = -38cos19 + 29cos55 = -19.29598922
    Fy = 38sin19 + 29sin55 = 36.12699915

    Resultant vector = sqrt [ (-19.29598922)2 + (36.12699915)2]
    Resultant vector = 40.95723706 meters

    Θ = tan-1(36.12699915/-19.29598922)
    Θ = 61.89263517 degrees N of W

    Those are my answers but apparently they are wrong. The provided answers are 53.8 km, 12.2 ° from east. Where am I going wrong? Thank you in advance :)
  2. jcsd
  3. Sep 16, 2011 #2


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    You determined A + B. I think you want B with respect to A. Draw a diagram of what is going on and you may see the solution.
  4. Sep 16, 2011 #3
    Isn't A+B the distance between A and B?
  5. Sep 16, 2011 #4
    I drew a diagram from the very beginning and still don't see my error.
  6. Sep 16, 2011 #5


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    No. It is a vector sum. I think you want a vector difference.
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