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Simple vector question

  1. Oct 7, 2013 #1
    1. The problem statement, all variables and given/known data

    The resultant of vectors A and B has a magnitude of 20 units. A has a magnitude of 8 units, and the angle between A and B is 40 degrees. Calculate the magnitude of B.

    2. Relevant equations

    Trig, resolving vector components.

    3. The attempt at a solution

    I worked out the equations and got |B| = 13.20 units. But, this isn't any of my choices. Am I right, or am I missing something here?
     
  2. jcsd
  3. Oct 8, 2013 #2

    ehild

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    Your result is correct.

    ehild
     
  4. Oct 8, 2013 #3

    Dick

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    That's what I got. But maybe we made the same mistake? Mind showing you you got that?
     
  5. Oct 8, 2013 #4
    Sure. Align A along the +x axis, with B at 40 degrees above that.

    Then:

    Ax = 8
    Ay = 0
    Bx = Bcos(40)
    By = Bsin(40)

    So Rx = 8+Bcos(40)
    Ry = Bsin(40)

    The magnitude of the resultant R would be sqrt(Rx^2 + Ry^2), which is equal to 20, so

    20 = sqrt((8+Bcos(40))^2 + (Bsin(40))^2). Solving for B yields 13.20.

    For the record, my choices were

    12.6
    16.2
    14.8
    18.4

    But I don't see how you could get any of them.
     
  6. Oct 8, 2013 #5

    Dick

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    Same thing I did. If ehild got the same result as us I have little doubt that it's correct. Probably just a mistake in the choices.
     
  7. Oct 8, 2013 #6
    Awesome, thanks.
     
  8. Oct 8, 2013 #7

    ehild

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    I used Cosine Law, with 140°angle between vectors A and B, and got the same result.

    ehild
     
  9. Oct 8, 2013 #8

    ehild

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    I used Cosine Law, and got the same result.

    ehild
     
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