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Finding the magnitude/direction of a resultant vector?

  1. Aug 25, 2013 #1
    1. The problem statement, all variables and given/known data
    Four vectors A, B, C, and D are shown (not to scale). Vector A has magnitude 20.0 and acts at an angle of 12.9 degrees with respect to the positive x axis. Vector B has magnitude 15.0 and acts at an angle of 55.7 degrees with respect to the positive x axis. Vector C has magnitude 31.5 and acts at an angle of 146.5 degrees with respect to the positive x axis. Vector D has magnitude 13.0 and acts at an angle of 296.4 degrees with respect to the positive x axis.

    Question: What are the magnitude and direction of the resultant vector, R, when the parallelogram law is applied to A and B?

    2. Relevant equations
    Law of Sines and Law of Cosines..
    A/sina=B/sinb=C/sinc
    C=sqrt(A^2+B^2-2ABcos(c)

    3. The attempt at a solution

    I solved for The resultant vector and got 32.6 N.... R=sqrt(20^2 +15^2-2(20*15*cos(137.2)))
    Then I used law of sines to find the direction and got 52.5 degrees.

    Apparently, I'm wrong. I recalculated all the angles not given and they seem to be right, but my end result ends up being wrong. Any tips?
    Thank you!
     

    Attached Files:

  2. jcsd
  3. Aug 25, 2013 #2

    lewando

    User Avatar
    Gold Member

    You might want to post more detail on what you did here. That's where the problem lies.
     
  4. Aug 25, 2013 #3
    Alright, sorry! I did 32.6/sin(r)=15/21.4.
    I got 21.4 from the calculating the angle 1/2(ThetaB-ThetaA)
     
  5. Aug 25, 2013 #4
    It will be a lot easier to find the components of each vector, then add them component-wise, then find the magnitude and direction of the resultant.
     
  6. Aug 25, 2013 #5
    Thanks! You're right that was easier. I got it :)
     
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