Help me with this problem.. impulse and momentum

Question

radicalsniper · Answer

attachment

amistre64 · Answer

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the forward velocity seems to be equal to some adjusted version of V cos($\alpha$)

radicalsniper · Answer

I want to apply the conservation of momentum in the line of action of "v" in your illustration. Any thoughts?

vincent-lyon.fr · Answer

You must apply conservation of horizontal momentum.

radicalsniper · Answer

Can you help me with the general equation? I am having a hard time writing it correctly.. 
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By the way, can I do it with respect to the n-axis(in the drawing)? I'll just add the impulse in state 1? I got an answer if I tried the horizontal momentum.. I just like to try a different approach