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Homework Help: Find the angle that the vector R

  1. Sep 7, 2003 #1
    part 1 of 2
    Two vectors A and B, are lying in the xy
    plane and given by
    A = Axi +Ayj
    B = Bxi +Byj
    (x y are subscripts)

    where A x = 4.4 m, A y = 1.74 m, B x = 7.58 m, B y = -6.76 m. Let R = A+B.
    Find the magnitude of R. Answer in units
    of m.

    So it is
    A = 4.4mI + 1.74mJ
    B = 7.58mI - 5.02J

    I have found out R by using the distance formula
    sqrt(11.98^2 + 5.02^2) = 12.9893 m(which is right)

    part 2 of 2
    Find the angle that the vector R makes from
    the positive x axis. Choose your answer to be
    between -180 # and +180 # . The positive an_
    gular direction is counter clockwise measured
    from the x axis. Answer in units of # .

    I tried this problem using the cosine law.
    -5.02squared-11.98squared-12.99squared
    ______________________________________(division)
    -2*11.98*12.99

    I got 22.73 degrees. But when I sumbit this answer, it says I'm wrong. Can you figure out what I'm doing wrong?
     
  2. jcsd
  3. Sep 7, 2003 #2

    HallsofIvy

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    Science Advisor

    The angle you are looking for, the angle the vector R makes with the x-axis is NOT an angle in the triangle formed by the three vectors. Also, you have the cosine law wrong (it may be a typo).
    It is a^2= b^2+ c^2- 2bc cos(A) so cos(A)= (a^2- b^2- c^2)/(2bc).

    In any case, the simplest way to do this is to look at the vector
    R only. You know the components of R. Look at the right triangle formed by the vector and it's components and think "tangent"!
     
  4. Sep 7, 2003 #3

    enigma

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    Staff Emeritus
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    Gold Member

    By is incorrect (it's the y-comp of R), but it looks like you caught that in the next part.

    Just find the arctan. rise/run = tan θ , so atan (rise/run) = θ

    Be sure you know what quadrant you're in. atan is only defined for +- 90 degrees, so you will need to add 180 degrees if you're in the second or third quadrants.
     
  5. Sep 7, 2003 #4
    After I did that I got 22.74, the same answer as I did before, which is wrong.
     
  6. Sep 7, 2003 #5
    The answer was -22.74(QIV), which is same as 22.74(QI)
     
  7. Sep 8, 2003 #6

    HallsofIvy

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    Science Advisor

    Why is "-22.74(QIV)" the same as "22.74(QI)"? They look very different to me!
     
  8. Sep 8, 2003 #7
    I figured that out last night, I thought the problem said that answer has to be between 0 and 180 but then realized that it was between -180 and 180.
     
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