A horizontal spring with spring constant {eq}100\ N/m {/eq} is compressed {eq}20\ cm {/eq} and used to launch a {eq}2.5\ kg {/eq} box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is {eq}0.15 {/eq}.

A. What is the speed of the box immediately after it loses contact with the spring?

B. Find the change in kinetic energy of the box when it comes to a stop.

C. Draw the free body diagram of the block when it is on the rough surface.

D. Use work and energy to find how far the box slides across the rough surface before stopping.