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Did I add the vectors right?

  1. Aug 31, 2007 #1
    This one is giving me a headache.
    Pretty sure i am wrong somewhere.
    Did I add the vectors right?

    1. The problem statement, all variables and given/known data
    Vector A is 100 units at 30 degrees.
    Vector B is 200 units at 140 degrees.
    Find the vector sum R: R=A=B



    2. Relevant equations



    3. The attempt at a solution
    So this is where I am:
    100cos30 =86.6
    100sin30 = 50

    200cos140= -153
    200sin140= 128.55

    Add the X and Y's
    86.6 -153= -67
    50+128.55 = 178.55

    Using Pyth. Thereom -67^2+ 178.55^2 = 165.5
    so R= 155.5 units

    Angle=
    Tan (178.55/-67) then take the inverse Tangent = 75 degrees
     
  2. jcsd
  3. Aug 31, 2007 #2

    learningphysics

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    You made a mistake with the pythagorean theorem. You should be squaring the entire component... ie: it should be:

    (-67)^2 + 178.55^2

    Not -(67^2) + 178.55^2

    And the inverse tan is wrong.
     
  4. Aug 31, 2007 #3
    Why is the inverse tan wrong?
     
  5. Aug 31, 2007 #4
    You didn't take into account the sign. tan(75) > 0, whereas you got something negetive.
     
  6. Aug 31, 2007 #5

    learningphysics

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    Yes, and arctan(178.55/67) = 69.43 not 75...

    You need to use the fact that the angle is in the second quadrant, to get the exact angle... so it's 180-69.43 = 110.57.
     
    Last edited: Aug 31, 2007
  7. Aug 31, 2007 #6
    first and foremost you cant ignore the sign because negative arctan is in the 4th quadrent and the positive of that is in the 2nd quadrent. Ignoring the negative is something you cannot do.
     
  8. Aug 31, 2007 #7

    learningphysics

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    Yes, I know. I'm just pointing out that there's another mistake on top of the sign mistake.
     
  9. Aug 31, 2007 #8

    learningphysics

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    Don't you mean positive tan is the 1st and 3rd quadrant... negative tan is the 2nd and 4th quadrant?
     
  10. Aug 31, 2007 #9
    What mistake are you pointing out because you said to ignore the sign and you dont get the get the answer. If it is -75 you have to add 180 to get the angle in the right position which is 105 definately different than 75. IS the answer negative or positive??

    one more thing is that r=a=b or r=a+b?
     
  11. Aug 31, 2007 #10
    Yes but when you enter arctan in a calculator it gives you the answer in either the first or 4th quadrent.
     
  12. Aug 31, 2007 #11

    learningphysics

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    I was not telling him to ignore the sign. I said even if you ignore the sign...

    Because arctan(178.55/-67) is not -75. It is -69.43. That is the mistake I was referring to.

    So then the angle is 180-69.43 = 110.57.
     
  13. Aug 31, 2007 #12
    Ok I got you it just seemed that way.

    I got the same thing by the way.
     
  14. Aug 31, 2007 #13

    learningphysics

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    Yeah, I'm sorry. Poor choice of words... I'll edit the earlier post so he doesn't get confused.
     
  15. Aug 31, 2007 #14
    Thank you all very much!
     
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