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Vectors- Im really stuck

  1. Apr 10, 2006 #1

    danago

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    Hey. Heres the question:

    Two boats are moving along straight paths and their position vectors at noon are:

    For the first question, i assumed its initial position would be 0 hours after noon. So i just answered it as:

    [tex]7\mathbf{i}-5\mathbf{j}[/tex]

    Now i wouldnt have a clue if thats even close to being correct, but its the only decent answer i could come up with.

    For the next part, i drew the diagram, and just found a vector going from the position of the first boat to the second, from the initial positions, which gave me the final vector:

    [tex]4\mathbf{i}+18\mathbf{j}[/tex]

    For part c, the velocity of the second boat, i just wrote how much the position vector increases for every incriment of t. I came up with:

    [tex]-3\mathbf{i}-\mathbf{j}[/tex]

    The problem with this was that the question said they were travelling in a straight line, and if i apply this velocity, then they change their direction. So im lost.

    And with the final question, im stuck, because i cant really do it until i answer the previous ones correctly.

    So if anyone doesn't mind, please put me on the right track for these questions, because i highly boubt ive answered them correctly.

    Thanks,
    Dan.
     
  2. jcsd
  3. Apr 10, 2006 #2
    You're first and third answers are right. The second should be 5i + 13j
    I don't see a problem there. It's a constant vector.

    And for the last part, what's the relation between the position vectors of the boats when they collide?
     
  4. Apr 10, 2006 #3

    danago

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    could you explain how you got 5i + 13j please? I re did it, and ended with the i component being 5, but i dont understand how you got 13 for the j component.

    And ill try the final question now.
     
  5. Apr 10, 2006 #4
    Sorry, that was a typo. :redface:
     
  6. Apr 10, 2006 #5

    danago

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    so its 5i + 18j then?

    Anyway, im doing the final question now. So to find when they collide, i need to find then their position vectors are the same, at the same value for t.

    So do i just equate the components for each vector?:
    i 7-4t
    j -5+t

    i 12-3t
    j 13-t

    So then i need to find when the i and j components of both ships are the same. I got that when the i component of both boats is 27, the j component will be 4, so they will collide at:

    [tex]27\mathbf{i}+5\mathbf{j}[/tex]

    Im not sure if thats right :S
     
  7. Apr 10, 2006 #6

    Hootenanny

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    I found that the boats do not collide.

    -Hoot
     
  8. Apr 10, 2006 #7

    Hootenanny

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    You can check if your answer is correct (whether they collide at your defined point), choose a vector equation and sub your values in for i and j such as this;

    [tex]r_{1} = (7-4t)j + (t-5)j[/tex]

    Subbing [itex]27i + 5j[/itex] into each component;

    [tex]7 - 4t = 27[/tex]

    [tex]t - 5 = 5[/tex]

    Now, do they both return the same value of t?

    -Hoot
     
  9. Apr 10, 2006 #8

    danago

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    yea i thought about it again, and no, they dont give the same values of t. Thanks for the help everyone :)
     
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