Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 36

36 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 $D = 2.20 \text{ m}$ from the edge of the table; see Fig. 8-36. Bobby compresses the spring $1.10 \text{ cm}$, but the center of the marble falls $26.3 \text{ cm}$ short of the center of the box. How far should Rhoda compress the spring to score a direct hit? Assume that neither the spring nor the ball encounters friction in the gun.