# Velocity vectors in different directions for momentum

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1. Feb 13, 2015

### jb007

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.

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. Feb 13, 2015

### Orodruin

Staff Emeritus
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:
$$(A\hat i + B \hat j) + (C\hat i + D\hat j) = (A+C)\hat i + (B+D)\hat j.$$

3. Feb 13, 2015

### jb007

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.

4. Feb 13, 2015

### BvU

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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