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Relative Motion and Vectors

  1. Sep 16, 2008 #1
    1. The problem statement, all variables and given/known data
    Car A's velocity varies as Va=3t^2i + 3tj
    Car B's velocity varies as Vb= -4ti + 4t^2j
    Both car's start at t=0.

    a) Find the position of Car A with respect to Car B at t=1 second.
    b) Find the velocity of Car B with respecto Car A at t=2.

    3. The attempt at a solution

    a) I began by finding the antiderivative of Va and Vb.
    I got v'(A)=t^3i + 3/2t^2i and
    v'(B) = -2t^2i + 4/3t^3

    Then I plugged in 1 for t and subtracted Car A - Car B.
    I got 3i - 1/6j
    Did I do that right?

    b) I basically did the same thing except I used to orginial equations, plugged in 2 for t, abd subtracted Car B- Car A.
    I came up with 4i - 24j

    Did I do those problems correctly?
  2. jcsd
  3. Sep 16, 2008 #2
    well you messed up with the components i and j in your integrals. You have 2 i's and no j for the first one, and no j in the second one.
    But, I think you just typed it wrong so don't worry about it.

    For part a I got the same thing you did except positive. I got 3i + 1/6j
    and I didn't do the second part, but you might want to double check that that one isn't also positive, like 4i + 24j
  4. Sep 16, 2008 #3
    Okay, so instead of subtracting vectors in relative motion, I should add them?

    When I plotted the vectors I did positive js.

    Oh and sorry about the mistype!
  5. Sep 16, 2008 #4
    no, you still subtract them. But should get I think it was 9/6j - 8/6j = 1/6j positive.
    So you did it right, maybe you just switched the vectors or got confused somewhere.
  6. Sep 17, 2008 #5
    Ok, so, when I work out the components of the vectors, that is what I should subtract?

    For instance, I would do:
    3/2j - 4/3j

    Because I have been adding both i's and both j's and then subtracting those numbers from eachother.
  7. Sep 18, 2008 #6
    either way works.
    because if you have say 4i + 6j
    and I want to subtract the vector 2i + 3j
    it would be written like
    (4i + 6j) - (2i + 3j)
    which is equal to
    4i + 6j - 2i - 3j = 2i + 3j

    But to make it easier on yourself you can use a different form of representing vectors: (i, j) without the plus.
  8. Sep 18, 2008 #7
    Okay, thank you!
    I don't know how to mark this as solved.
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