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Finding Magnitudes of Vectors

  1. Sep 5, 2010 #1
    I am pretty good at this but this one seems impossible to figure out. Can anyone help?

    Vector A has a magnitude of 188 units and points 30 degrees north of west. Vector B points 50 degrees East of North. Vector C points 20 degrees West of South. These three vectors add to give a resultant vector that is zero. Using COMPONENTS method, find the magnitudes of Vector B and Vector C.

    Thanks in Advance!
     
  2. jcsd
  3. Sep 5, 2010 #2

    CompuChip

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    First of all DRAW A PICTURE.
    That's about the first rule in vector problems.

    Next, let me give you some small sub-problems to get you started... can you rewrite the directions of A, B and C as angles with respect to the x-axis (i.e. east direction)?
    Assuming that |B| and |C| are the magnitudes of vector B and C respectively, can you write down what the x- and y-components (Ax, Ay, Bx, By, Cx, Cy) of the three vectors will be?
    What relations between these components follow from the resultant being zero?
     
  4. Sep 5, 2010 #3
    Thanks for the reply CompuChip. I am finding it difficult to find 2 variables (the magnitudes of B and C) based on a couple of other variables.

    My Physics teacher wrote this to help us out.

    Rx=Ax+Bx+Cx
    =()+()B+()C

    Ry=Ay+By+Cy
    =()+()B+()C

    I understand that this is how the problem reads numerically, but I don't understand how to solve.
     
  5. Sep 5, 2010 #4
    Ok so I did the problem graphically and obtained the correct answers. I verified these answers by plugging them into the calculator. How would I show my work on paper?
     
  6. Sep 5, 2010 #5

    CompuChip

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    Officially, you can solve the system of two equations in two unknowns.

    For example, you can rewrite equation (**) to an equation for either B, or C, for example: B = (Ry - () - ()C) / (). Then you can replace B in equation (*) and solve the remaining equation in one variable for C.
     
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