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Homework Help: 3 vectors using south, northeast, and west

  1. Feb 14, 2008 #1
    [SOLVED] 3 vectors using south, northeast, and west

    1. The problem statement, all variables and given/known data
    A particle undergoes the following consecutive displacements: 3.80 m south, 8.40 m northeast, and 14.0 m west. What is the resultant displacement?


    2. Relevant equations



    3. The attempt at a solution

    This means that I have 3.80j, 8.4i, and 14.0k, right? I could then add up all of the x components and y components, right? or do I need to use the law of cos?

    thank you very much
     
  2. jcsd
  3. Feb 15, 2008 #2

    Kurdt

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    No. This is a 2D problem. Conventionally you would have -3.8j for south and -14.0i for west. North East will be a vector of components of i and j. Try drawing a diagram to help you.
     
  4. Feb 15, 2008 #3
    Thank you very much

    I drew a diagram, but the triangle does not seem to be a perfect right triangle. Wouldn't I also have 8.4k? Could you tell me what formula I would need to solve this problem? or would I need to draw it out on graph paper and measure the angles?

    Vector A would be (0i+3.8j),vector B would be 8.4k , and vector C would be (14.03i+oj), right? or is the 8.4 part extra information that it is not needed?

    I added up the components and got:

    Vector A+B=14.03i+3.8j

    R=square root of (14.03)^2+(3.8)^2=14.5

    Does that look correct? How would I go about solving for the angle?

    Thank you
     
    Last edited: Feb 15, 2008
  5. Feb 15, 2008 #4

    Kurdt

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    The northeast vector will have i and j components. Northeast indicates the vector is 45 degrees north of east, so the components will be equal.

    The other two vectors will have negative components in standard notation since i is taken to be the direction east and j is taken to be in the north direction.

    Then one will use vector addition to find the resultant displacement.
     
  6. Feb 15, 2008 #5
    Thank you very much

    I found the x and y components of the northeast vector to be 5.9. I then added up the i's and j's and got 19.93 for the i's and 9.7 for the j's.

    Magnitude=square root (19.93)^2+(9.7)^2=22.2

    direction=45°

    Does that look right?

    Thank you very much
     
  7. Feb 15, 2008 #6

    Kurdt

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    South and west are negative, so for the i's it would be 5.9 + (-14.0) etc.
     
  8. Feb 19, 2008 #7
    Thank you very much

    Regards
     
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