How Far Should Rondo Compress the Spring to Hit the Target?

[bballcool34]

Here's the question:

Two children are playing a game in which they try to hit a small box on the floor with a marble fired from a spring-loaded gun that is mounted on a table. The target box is horizontal distance D = 2.20 m from the edge of the table. Bobby compresses the spring 1.1 cm, but the center of the marble falls .27 m short of the center of the box. How far should Rondo compress the spring to score a direct hit? (assume that neither spring nor ball encounters friction).

I know the general gist of how to solve the problem---Find spring potential energy of Bobby, set that equal to K, and do the same for Rhonda. However, I don't understand WHY I'm supposed to do this. Why does spring potential energy = KE in this problem? If anyone could explain it to me, that'd be great:

 

[rock.freak667]

If you are ignoring frictional effects, then the only other energy conversion taking is place is the conversion of the potential energy to kinetic. If that did not happen, then after the spring is released the ball would not move now would it?