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Homework Help: What's wrong with this?

  1. Sep 16, 2010 #1
    I have to find the resultant of:

    [PLAIN]http://img17.imageshack.us/img17/8263/68709011.jpg [Broken]

    So I decided to break it up into components:

    [PLAIN]http://img37.imageshack.us/img37/7032/71250823.jpg [Broken]

    (The black arrow in the first picture is the blue arrow in the second, that's the way I did it!)

    I found the blue line in the picture using the cosine rule:

    [itex] c \ = \ \sqrt{30^2 \ + \ 40^2 \ - \ (2 \cdot 30 \ \cdot \ 40 \ \cdot \ \cos(120)) [/itex]

    c = 60.827 and it's just horizontal along the x-axis.

    Then I added c = 60.827 to the third vector:

    [PLAIN]http://img96.imageshack.us/img96/1917/92586648.jpg [Broken]

    I found the white arrow, the total resultant, using the same technique:

    [itex] d \ = \ \sqrt{25^2 \ + \ 60.827^2 \ - \ (2 \cdot 25 \ \cdot \ 60.827 \ \cdot \ \cos(105)) [/itex]

    d = 71.5

    My book says the answer is 67.6

    I got the angle of the resultant using the sine rule:

    [itex] \theta \ = \ \sin^{-1} ( \frac{25 \cdot \sin(105)}{60.827} ) \ = \ 23.39 [/itex]

    My book says the angle is: 11.3°

    What did I do wrong?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 16, 2010 #2
    Where did you get 105? Clearly the most straightforward way to do this is to break it up into components, i.e. x=30cos45+40cos15+25sin15
    y=30sin45-40sin15-25cos15
    r^2=x^2+y^2
    theta=arctan(y/x)
     
  4. Sep 16, 2010 #3
    The 105° comes from adding the 90° angle under the red vector in third picture with the
    15° the blue vector is making, giving 105°.

    The problem was asked to be solved in component form but I tried it this way & got
    the wrong answer, I can't see why & am totally stumped & would just like to know
    why.
     
  5. Sep 16, 2010 #4
    I don't know, round off errors most likely. Components are the way to go, less calculations.
     
  6. Sep 16, 2010 #5
    Yeah I had a good look at it & realised I'd assumed too much, I didn't calculate the
    angle of the first resultant vector, I got a better answer, thanks!
     
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