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Vector and component vectors

  1. Mar 27, 2015 #1
    1. The problem statement, all variables and given/known data
    Use the component method to add the vectors vector A and vector B shown in the figure. The length of vector B is 3.25 m and the angle θ = 28.5°. Express the resultant vector A + vector B in unit-vector notation.

    p1-38alt.gif

    2. Relevant equations
    x = rcos
    y = rsin

    3. The attempt at a solution
    I drew the components for vector A, and got Ax = 3cos28.5 = 2.64m and Ay = 3sin28.5 = 1.43m ( i don't know if they are correct though). I'm lost at what to do next for vector B cause its a vertical line.

    Is it right for me to say that after finding vector B's components, i add the X components to find i unit vector and add the Y components to find the j unit vector? And i just get the answer by putting them in one equation, i + j?
     
  2. jcsd
  3. Mar 27, 2015 #2
    Well, if it's perpendicular to the x axis think of what is the angle for it's measure (if the positive x-axis is 0)?
     
  4. Mar 27, 2015 #3
    I don't know if i'm answering your question, but is it 90 degrees..?
     
  5. Mar 27, 2015 #4
    Yes. Good. So now you can calculate the components of the B vector. It's ok if one of them is zero.
     
  6. Mar 27, 2015 #5
    I'm not so sure about how to calculate the components. As in isn't there not enough information?

    I don't know if i can just assume Bx = 0 and By = 3.25m, but if i can, will it be Ax + Bx = 2.64 + 0 = 2.64i and Ay + By = 1.43 + 3.25 = 4.68j?
     
  7. Mar 27, 2015 #6

    Matternot

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    Gold Member

    It is 90 degrees but think about what x=rcosθ and y=rsinθ actually means; don't just plug into the formulae and hope.

    The vector is being split up into 2 vectors in perpendicular directions: (x,y). Here you calculated A as (2.64m,1.43m). This means, if I move 2.64 in the x direction and 1.43 in the y direction, you will end up where the vector points (i.e. 3m away at 28.5 degrees).

    If my vector was (a,b) and I wanted to add (c,d) to it, this means going a in the x direction, then b in the x direction, then c in the x direction, then d in the y direction. This is clearly a+c in the x direction and b+d in the y direction. Therefore this results in (a,b)+(c,d)=(a+c,b+d).

    If B is a vertical line, it only has a y component. You don't need to travel in the x direction at all to reach the end of the arrow. This means the vector will be (0,3.25). i.e. 0 in the x direction, 3.25 in the y direction. It is easier to think about this than the angle and magnitude of b.

    You are therefore doing the addition A+B=(rcosθ,rsinθ)+(0,By), which I shall leave to you to calculate.

    I hope this helps.
     
    Last edited: Mar 27, 2015
  8. Mar 27, 2015 #7
    I think I understand but am a little confused at the same time. It did help me in understanding why By = 0 though! And by A+B=(rcosθ,rsinθ)+(0,By), you do mean that I add the x components and y components separately, am I correct?
     
  9. Mar 27, 2015 #8

    Matternot

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    Exactly. They can be added separately.

    This is because if my vector was (a,b) and I wanted to go one more step in the x direction, the y value wouldn't be effected at all. my new vector would be (a+1,b)

    You can also think of (a,b) as (a,0)+(0,b) if that helps. Then (a,b)+(1,0) is the same as (a,0) + (1,0) + (0,b) = (a+1,0)+(0,b) = (a+1,b)

    As I said before, (a,b)+(c,d) = (a+c,b+d)
    Here the x and y components are being added seperately
     
  10. Mar 27, 2015 #9
    Alright, I think I get it! Thank you so much. Hopefully I'll get the right answer
     
  11. Mar 27, 2015 #10

    Matternot

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    Cool!

    If you post your final answer, I'll happily confirm if it's correct or not
     
  12. Mar 27, 2015 #11
    I got 2.64i + 4.68j , is that correct? I added (Ax + 0, Ay + By) for that answer and wrote it in unit vectors.
     
  13. Mar 27, 2015 #12

    Matternot

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    Yep, you've got it :smile:
     
  14. Mar 27, 2015 #13
    Awesome, thanks for the help! :)
     
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