Angular impulse

1. The problem statement, all variables and given/known data
A thin rod of length L, mass m is suspended horizontally at rest. It is suddenly released and experiences immediately after an impulse vertically upwards at one end.

I need to find the maximum height reached by the centre of mass and the angular velocity of rotation about the centre of mass.

3. The attempt at a solution
I can’t see how there is enough information given in the question. I have used the fact that J=0.5Lp here (J is angular momentum) from the relation between angular and linear impulse, and then this means 0.5Lmv=Iω, with I=mL2/12. Then 0.5Lmv=mL2ω/12. This relates v and ω by v=ωL/6. I could then probably work with constant acceleration formulae to get the answer, however both v and ω are unknowns (and I have to find ω in the next part) so I have no idea where to go.

Thanks in advance 🙂

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