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Adding Vectors

  1. Sep 26, 2009 #1
    1. The problem statement, all variables and given/known data
    Vector A points in the negative x direction. Vector B points at an angle of 30 degrees above the positive x axis. Vector C has a magnitude of 15.0 m and points in a direction 40 degrees below the positive x axis. Given that vectors A + B + C = 0, find the magnitude of vector A and vector B


    2. Relevant equations
    Sin = opp/hyp


    3. The attempt at a solution
    For vector C, I found the x direction to be 11.49 m and the y direction to be -9.64 m.

    Other than that I have no idea where to begin.

    thanks,
     
  2. jcsd
  3. Sep 26, 2009 #2

    rock.freak667

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    Good. So we know C=11.49i-9.647j

    so lets put A=ai+bj. It says A points in the negative x direction, so what should A really be ? (i.e. should the 'a' be +a or -a and what should 'b' equal to?)

    So B acts at an angle of 30 degrees to the x-axis. If the magnitude of B is |B| then B=|B|(ci+dj)

    so find A+B+C, grouping together the i and j terms.
     
  4. Sep 26, 2009 #3
    like this ?

    C = 11.49i - 9.647j
    A = ai - bj
    B = |B| (ci + dj)
    _____________________ +

    = (11.49 + a + |B|c)i - (9.647 - b + |C|d)j

    Is that right? :confused:
     
  5. Sep 26, 2009 #4

    rock.freak667

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    Sorry I made a mistake, let's take out the |B| and just have B=ci+dj

    You should get A+B+C = (11.49+a+c)i + (-9.647-b+d)j

    once again now, if A=ai+bj is in the negative x direction, what is b equal to? And what sign should the a really have ?
     
  6. Sep 26, 2009 #5
    the "a" should be negative so A=-ai+bj, should the b also be negative?
     
  7. Sep 26, 2009 #6

    rock.freak667

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    right the 'a' should really be '-a'. So if the j component is the vertical component, and you know A is purely horizontal, what value should 'b' equal to?
     
  8. Sep 26, 2009 #7
    b should be 0 in the A vector

    C = 11.49i - 9.647j
    A = -ai
    B = ci + dj
    _________________ +

    = (11.49 -a + c)i + (-9.647 + d)j = 0

    Is that correct? whats the next step?

    Thank you
     
  9. Sep 26, 2009 #8

    rock.freak667

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    yes this correct. So if it is equal to zero, that means both the i and j components are zero, so what is d?
     
  10. Sep 26, 2009 #9
    d= oi + oj

    how does it get me to find the magnitude of A and B vectors?
     
  11. Sep 26, 2009 #10

    rock.freak667

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    no no

    we have A+B+C = = (11.49 -a + c)i + (-9.647 + d)j = 0 =0i+0j.

    so when you equate components, what is d equal to?
     
  12. Sep 26, 2009 #11
    d is zero?
     
  13. Sep 26, 2009 #12

    rock.freak667

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    no if (-9.647 + d) =0 what is d? Do you know why (-9.647 + d) equal 0?
     
  14. Sep 26, 2009 #13
    sorry d is 9.647
     
  15. Sep 26, 2009 #14

    rock.freak667

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    ok good. Now we know for a vector say R of magnitude |R|, acting at an angle θ to the x-axis can be represented as R= |R|cosθi+|R|sinθj


    Can you now make a similar comparison to the vector B with magnitude |B|? Are you able to see how 'd' relates to |B| at the given angle?
     
  16. Sep 26, 2009 #15
    vector B = |B|cos30i + |B|sin30j ?
    is 9.647 the y component of vector B?
     
  17. Sep 26, 2009 #16

    rock.freak667

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    yes, so now if d=|B|sin30 -> 9.647=|B|sinn30 what is |B| equal to?

    When you get |B|, can you find what 'c' is equal to ?
     
  18. Sep 26, 2009 #17
    |B| = 11.139i + 19.294j?
     
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