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Vector, velocity, and parallel

  1. Jan 22, 2009 #1
    1. The problem statement, all variables and given/known data

    A 100 meter dash is run on a track in the direction of the vector v = 4i + 7j. The wind velocity w is 5i + j km/hr. The rules say that a legal wind speed measured in the direction of the dash must not exceed 5 km/hr.

    Find the component of w which is parallel to v.

    2. Relevant equations



    3. The attempt at a solution

    I have no idea to solve this problem
     
    Last edited: Jan 22, 2009
  2. jcsd
  3. Jan 22, 2009 #2

    Hootenanny

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    You must have some idea. Which operation gives to the component of one vector that is parallel to another?
     
  4. Jan 22, 2009 #3
    it's parallel to one another if it's angle between them is 0 right?

    so therefore using the geometric of vectors:

    v . w = |v| * |w|, right?
     
  5. Jan 22, 2009 #4

    gabbagabbahey

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    Sure, if v . w = |v| * |w| then w and v are parallel; but that's not what Hootenanny was asking.

    Suppose you want to find 'the component of w' that is parallel to v....how would you do that?
     
  6. Jan 22, 2009 #5

    Hootenanny

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    That is correct. However, it is perhaps more useful to note that:

    [tex]\mathbf{v}\cdot\left(\frac{\mathbf{w}}{\left\|\mathbf{w}\right\|}\right) = \left|\mathbf{v}\right|\cos\theta[/tex]

    That is, if u is a unit vector then the scalar product v.u gives the projection of v in the direction u.

    Edit:
    :grumpy:
     
  7. Jan 22, 2009 #6
    hmmm...so how do I apply this to the question?
     
  8. Jan 22, 2009 #7

    gabbagabbahey

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    o:) o:) o:)
     
  9. Jan 22, 2009 #8
    Is this question asking for a new wind speed/vector which is parallel to v
     
  10. Jan 22, 2009 #9

    Hootenanny

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    No. The question is asking for the component of w that is parallel to v. Can you use the hints I have you in post number 5 to solve this problem?
     
  11. Jan 22, 2009 #10
    No, I don't....
     
  12. Jan 23, 2009 #11

    Hootenanny

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    I don't know how I can make it clearer without explicitly giving you the answer. Pay particular attention the the last paragraph in on of my previous posts.
     
  13. Jan 23, 2009 #12
    what is u related to my question?
     
  14. Jan 23, 2009 #13
    why is it v . w/||W|| not w . v/||v||
     
  15. Jan 23, 2009 #14

    gabbagabbahey

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    v . w/||W|| gives the component of v parallel to w.

    w . v/||v|| gives the component of w parallel to v.

    Since you are trying to find the component of the wind speed w parallel to the velocity v; you will indeed want to use w . v/||v|| for your problem.
     
  16. Jan 23, 2009 #15
    ok thanks! I got it now
     
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