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Homework Help: 2 vectors what third vector is needed to counter bakance the first 2?

  1. Jul 22, 2011 #1
    1. The problem statement, all variables and given/known data

    in the given figure, vectors u and v each have a magnitude of 55 pounds. Find the magnitude and direction of the force w needed to counterbalance u and v? So the "figure" is pretty simple... it shows a line labled North and south and vector u is pointing 45 degrees in the south west direction and vector v is pointing 60 degrees in the south east direction.

    2. Relevant equations

    trig functions

    3. The attempt at a solution

    this is a calc3 class using the varberg 9e text book and the class uses an online program called math lab which is provided by the text book and therefore all the online material directly relates to the text... So im on chapter 11 dealing with vectors... Specifically 3D vectors... however this appears to be a 2D problem... i missed a problem similar to this on my online quiz... so i went to the online practice problems and found this problem... and i clicked the "help me solve this" button which takes you step by step to the solution... At this point i could see where i made mistakes in solving the quiz problem, but i dont understand why i was wrong so my first question is... They come up with 67 pounds and so did i but they claim its at 277.5 degrees? or S7.5 degrees E? Why? wouldnt it be in the north east direction?
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jul 22, 2011 #2


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    Some things aren't clear. What does "vector v is pointing 60 degrees in the south east direction" mean? Maybe 60 degrees east of south? Or 60 degrees south of east?

    "they claim its at 277.5 degrees? or S7.5 degrees E?"
    277 degrees is probably measured clockwise from north, so it is 360-277 = 83 degrees west of north. I don't see how it could be S 7.5 E.
  4. Jul 23, 2011 #3
    Regardless of being east of south or south of east... i dont see how it can be S 7.5 E... Which was my question... however... it is east of south... and therefore i dont see how it can be 277.5 degrees... because the answer i come up with is 82.5 degrees north of east or of course that would be the same as 7.5 degrees east of north... so if you go clockwise 7.5+270=277.5 degrees which is their answer? that makes no sense... thats starting due east and measuring 277.5 degrees counter clockwise to the vector w...
  5. Jul 23, 2011 #4
    the only way i have been able to see it would be for it to the resultant vector of u and v... which would be 7.5 degrees east of south... and 277.5 degrees if starting at due east and measuring counter clockwise around to the resultant vector... just like you would normally measure degrees... but thats not what they asked for? right? it should directly opposite... i would think...
  6. Jul 23, 2011 #5
    or am i missing something? is this actually 3D? is north coming out of the page? and u and v are on the page? i wouldnt even know how to think about that?
  7. Jul 23, 2011 #6
    they say u=<-55sin45,-55cos45> i understand
    u=<-38.89,-38.89> i understand
    v=<55sin60,-55cos60> i understand
    v=<47.63,-27.50> i understand
    u+v=<8.74,-66.39> i understand
    w=-(u+v) i understand
    w=<-8.74,66.39> i understand
    ||w||=67 pounds (i understand)

    then inverse tan (66.39/-8.74)= 277.5 degrees (i dont understand)

    (am i missing something?)
  8. Jul 23, 2011 #7


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    277.5° is co-terminal with -82.5° (as measured from the positive x axis).

    That's correct for the resultant of u+v, but w = -(u+v), so w is 180° from u+v .
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