A student hangs two balls by a string, from a pulley connected with the roof of his house, as shown in the figure below. In the beginning, both the two balls are stationary at a height of 1.2 m from the ground. While the frictionless pulley of negligible mass is 5.2 m above the ground. Calculate the maximum height the lighter ball reaches if the system moves freely. 

[Hint: Evaluating the lighter ball's acceleration, calculate its speed when the other ball touches the ground. Think of it as its "launch" speed. Presume the balls don't collide with anything and the mass of the string is negligible.]