Energy and Momentum conservation, what else?

Note: there is no friction at all.

General problem:
A ball moves (in speed v1) toward a quarter of a circle (which was stand still before the ball touched it and can move on x) and walks on it until it leaves it.
How may I find the balls speed on x and y?

I have attached the following image to make the problem easier:

In this kind of questions, we use save of energy and save of linear momentum on x.

Using save of energy gives me the value of the ball’s speed But How may I get the speed on x direction and y direction of the ball?

Using save of momentum gives me an expression with two variables, the ball’s speed on x and the mass’s speed on x. (Which doesn’t help since I don’t know both of them)

Am I missing something here?