Pool Ball Collision: Solving for Angular Momentum and Friction

[Phizyk]

You have to use Pythagoras
$$v_{1}=\sqrt{v_{X1}^{2}+v_{Y1}^{2}}$$
where
$$v_{Y1}=v_{Y0}=v_{0}sin\alpha_{0}$$ in both cases and $$v_{X1}$$, which I counted.

 

[Anony-mouse]

Thanks everyone for your help, and thanks Phizyk for the equations. There is something I didn't understand.
$$\omega$$ is a vector right?
I don't see how to do this comparision $$v_{X0}<\omega_{0}R+2v_{Y0}\mu{(\frac{mR^{2}}{I}+1) }$$

Also, It seems weird to me that in the equation $$v_{X1}=v_{X0}-2\mu{v_{Y0}}$$, the angular velocity isn't involved in calculation $$v_{X1}$$. Is there something I'm missing?