A 5.0 kg box slides down a 5.0-m-high frictionless hill, starting from rest, across a 2.0-m-wide horizontal surface, then hits a horizontal spring with spring constant 500 N/m. The other end of the spring is anchored against a wall. The ground under the spring is frictionless, but the 2.0-m-wide horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.25.

a. What is the speed of the box just before reaching the rough surface?

b. What is the speed of the box just before hitting the spring?

c. How far is the spring compressed?

d. Including the first crossing, how many complete trips will the box make across the rough surface before coming to rest?