Launch angle affecting the splash height of a ball

Use the vertical velocity of the ball as it reaches the same height on the right hand side. By symmetry, this will be the vertical velocity (and horizontal) component of the projectile just as it leaves the cannon. What exactly do you want to calculate or need to know?

I believe you can model the situation crudely using simple energy conservation. Work out the total speed of the ball as it hits the water's surface and calculate its kinetic energy. Assume a mass $m_text{water}$ of the water rises above the surface due to the splash and write down the expression for its gravitational potential energy. Equate the two energies and solve for $h$, the height above the water's surface.

(Note: you might need to settle on a reasonable value of $m_text{water}$ first.)