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Vector resultant problem.

  1. Aug 30, 2012 #1
    1. The problem statement, all variables and given/known data

    A map suggests that Atlanta is d1 = 730 mi in a direction of θ1 = 5.12° north of east from Dallas. The same map shows that Chicago is d2 = 559 miles in a direction of θ2 = 21.0° west of north from Atlanta. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.

    2. Relevant equations

    trig functions

    3. The attempt at a solution

    i used the vector <65.1466, 727.087> for dallas to atlanta, and used the vector <521.87, 200.328> for atlanta to chicago. I added them together to get vector from dallas to chicago, then used the pythagorean theorem to get the resultant magnitude which was 719.542. The angle i got was 32.33 degrees by using inverse tangent of the dallas to chicago vector, then subtracted the 5.12 degrees to get the angle northeast of dallas. Still saying i have the wrong answer so i'm not sure what i'm doing wrong. please help
     
  2. jcsd
  3. Aug 30, 2012 #2

    Doc Al

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    Staff: Mentor

    To start with, it looks like you have mixed up your x and y components. (Assuming you mean it as x, y, where +x is east and +y is north.) And you need to be careful with signs.
     
  4. Aug 30, 2012 #3
    i see, so correcting my mistakes i should use <-200.3277, 521.8715> as my second vector. working the rest of the problem out accordingly gives me the resultant 788.7116 and the angle 41.9 degrees. i hope this is right, and also i'm still confused if i should use 41.9 degrees as the angle they are asking for or 41.9-5.12 = 36.78 as my answer?
     
  5. Aug 30, 2012 #4

    Doc Al

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    Staff: Mentor

    What's that angle measured from?
    Why would you subtract 5.12 ?

    Express the angle as X degrees north of east (or equivalently, Y degrees east of north).
     
  6. Aug 30, 2012 #5
    the angle would be 48.1 degrees north of east, correct?
     
  7. Aug 30, 2012 #6

    Doc Al

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    Staff: Mentor

    That sounds about right.
     
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