Calculating Moment of Inertia from Ball Angular Momentum Problem?

[togg]

Homework Statement

A 0.478-kg ball is thrown at a 22.3-cm tall, 0.383-kg object and hits with a perfectly horizontal velocity of 12.8 m/s. Suppose the ball strikes at the very top of the object. After collision the ball has a horizontal velocity of 4.6 m/s in the same direction. The object now has an angular velocity of 1.63 rad/s. If the object's center of mass is located 15.6 cm below the point where the ball hits, what is the moment of inertia of the object?

Homework Equations

I = MR^2

The Attempt at a Solution

I am honestly not sure where to begin on this one. I know the initial momentum is conserved and is proportional to the ball's mass and initial velocity. I was sick for the lecture and would appreciate any help on how to solve this problem.

Thanks

 

[haruspex]

There's a piece of information missing. I'll assume that there's no slipping at the base of the object.
This means that when the ball delivers an impulse to the top of the object, the object feels a horizontal impulse from the ground. The magnitude will be whatever is required to keep the bottom of the object stationary. You should be able to avoid worrying about that if you take moments about the base of the object (which you're allowed to do if that point is stationary).
So you just need the angular momentum equation for moments about the base. What net angular moment does the ball deliver? How does that relate to the acquired angular velocity?