A uniform cylinder with R=O.2 m and a mass of 2 kg is initially at rest on a ramp at a height of 3 meters above the ground. It then rolls down the ramp without slipping. (Use g=10 m/sz, |=(1/2) MR2) (a) (10 points) Find the linear acceleration of the cylinder as it rolls down the ramp. (b) (5 points) Find the rotational kinetic energy of the cylinder when it reaches the bottom of the ramp. 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 2.2 m horizontally from the edge of the table; see the figure below. Bobby compresses the spring 1.1 cm, but the center of the marble falls 27.0 cm short of the center of the box. How far should Rhoda compress the spring for the marble to hit the center of the box? Show your work. (Assume that neither the spring nor the ball encounters friction in the gun. Use g=10 m/s2.) [imam]