Solution:

First, calculate the velocity of the lower ball at the collision with the ground. We use the conservation of energy to find the velocity of the bottom ball at impact with the ground. We can equate the change in gravitational potential energy to the change in kinetic energy to find this velocity:

The following is a proof of why the velocity of the ball after colliding with the ground is equal in magnitude, but opposite in direction, but you don't have to know how to prove it.

OPTIONAL:

The basics is that since the Earth is so massive, that its change in velocity because of the collision is so small that it is negligeable, so the ball gets all the change.

First we use the conservation of momentum to give us one equation which we further simplify:

Now we use the conservation of energy to get a second equation which we also further simplify:

We can now replace of the energy equation with from the momentum equation:

Go back to the momentum equation and replace with . ( )

END OF OPTIONAL PART

Next, calculate the collision between and to get the final velocity, , of .
( and )
The initial velocity of the upper ball in the collision is the same magnitude as the the lower ball becaue they have both fallen the same distance.
We start with the conservation of momentum to get the first equation into which we plug the masses (note that we plug in for as was found above) and simplify:

Now we use the conservation of energy (in this case kinetic) for a second equation into which we also plug the masses and simplify:

We go back to the equation for from above and solve for and plug it into the simplified energy equation:

Now we have a big mess for simplifying and solving for .

Now we can use the quadratic equation to find :

The second value is the initial velocity, so the first value of is the final velocity of .
From the result of , obtain the max height of . We will find out how high above the collision point it goes (z) and then add on its initial height at impact of two times the radius of the lower ball at the end to find the final height above ground that the upper ball gets to (y).