One thing we should do first is set up a coordinate system. So for the record I've got an origin (which we really won't need) at the level of the water, and I've got a positive y direction pointing upward.

You've got more information than you might think you do. First, we know the initial velocity of the ball: it's 0 m/s because the child is dropping the ball, not throwing it. We also know the acceleration of the ball: 9.8 m/s^2 downward, or in our coordinate system a = -9.8 m/s^2.

What equation do we have that contains v0, v, a, and t?

v = v0 + at

v = 0 -9.8*2 = -19.6 m/s

So the velocity is 19.6 m/s downward when the ball strikes the water.

A final quick note: The acceleration of the ball is a = -9.8 m/s^2. g = 9.8 m/s^2. g is NEVER negative. This is a common notation mistake.

-Dan