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Difficult Vector problem

  1. Sep 7, 2009 #1
    < is the angle symbol here.

    R is the resultant of three forces A,B,C that is R = A+B+C
    If A = A<210, B=200 < Theta, C=200 <65, and R = 250 <125, use the component method to determine A and Theta.

    ok so I broke them into their components and now I have no idea how to find A and Theta

    Ax = A cos 30
    Ay = A sin 30
    Bx = 200 cos Theta or possibly could be 200 sin Theta
    By = 200 sin Theta or 200 cos Theta
    Cx=200 cos 65
    Cy = 200 sin 65
    Rx = 250 sin 35
    Ry = 250 cos 35

    A cos 30 + 200 cos Theta + 200 cos 65 = 250 sin 35

    A sin 30 + 200 sin Theta + 200 sin 65 = 250 cos 35

    would this be the correct approach? How in the world would you solve for A or Theta?
     
  2. jcsd
  3. Sep 7, 2009 #2
    [tex]Acos210+200cos\theta = 250cos135-200cos65[/tex]
    [tex]Asin210+200sin\theta = 250sin135-200sin65[/tex]
    You have two equations with two unknows, so you have a system and can find the variables.
     
    Last edited: Sep 7, 2009
  4. Sep 7, 2009 #3

    I am not really sure how to solve the system. I haven't taken linear algebra and surely havent dealt with any systems like this. Could someone please help
     
  5. Sep 7, 2009 #4
    Just solve for A and substitute.
     
  6. Sep 7, 2009 #5
    Solve one for A and the plug that into the other and then you can find theta.
     
  7. Sep 7, 2009 #6
    ok sounds simple enough..let me try and see
     
  8. Sep 7, 2009 #7
    ok maybe not so simple..I am going to have to pass on this. I cannot solve this system to save my life.

    I get

    A = (30.2 - 200 cos Theta)/cos 30

    and

    A=(23.4 - 200 sin Theta)/sin 30

    not even sure if this is correct..if I plug in A then I have Cos and Sin in one equation and not sure what to do with it.:confused:
     
  9. Sep 8, 2009 #8
    You know A in terms of [tex]\theta[/tex], so take one of your values for A and place it into the other equation. Then you'll have only constants and [tex]\theta[/tex] in the resulting equation.
     
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