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Velocity vectors in different directions for momentum

  1. Feb 13, 2015 #1
    1. The problem statement, all variables and given/known data
    I'm stuck on this problem, and I don't really know how to approach it.
    upload_2015-2-13_0-4-14.png

    2. Relevant equations
    Pretty much just p=mv
    And the conservation of linear momentum: total initial mv = total final mv

    3. The attempt at a solution
    I tried just plugging in the variables into the conservation of momentum equation, but it doesn't work out. I know you can't just add velocity vectors that are in different directions, right? They have to have the same I hat or j hat? How would you solve for them?
     
  2. jcsd
  3. Feb 13, 2015 #2

    Orodruin

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    What do you get when you try conservation of momentum? Can you show us your working? Vectors do add, but they add component by component, for example:
    $$
    (A\hat i + B \hat j) + (C\hat i + D\hat j) = (A+C)\hat i + (B+D)\hat j.
    $$
     
  4. Feb 13, 2015 #3
    So I used the conservation of p equation like this:

    mv0i + 2m0.5v0j = mvf + 2m0.25v0i

    But I know this must be wrong because the vectors here aren't adding by components.
     
  5. Feb 13, 2015 #4

    BvU

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    It's easier if you follow Oro's notation:$$
    m\; (v_0 \hat\imath + 0 \hat\jmath) + 2 m\; (0 \hat\imath + {\textstyle 1\over 2} v_0 \hat\jmath ) = ...$$This gives you two equations: one where you group all the ##\hat\imath## together -- this is the eqauation for conservation of momentum in the x direction -- and one where you group all the ##\hat\jmath## together

    From two equations you can solve for two unknowns: the ##\hat\imath## component gives you the velocity component in the x-direction and the ##\hat\jmath## idem y-direction. Together they are the velocity vector, with two components (one or both may be zero, of course).
     
    Last edited: Feb 13, 2015
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