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.