In a spring gun, a spring of force constant 400 N/m is compressed 0.15 m. When fired, 80.0% of the elastic potential energy stored in the spring is eventually converted into the kinetic energy of a 0.0590-kg uniform ball that is rolling without slipping at the base of a ramp. The ball continues to roll without slipping up the ramp with 90.0% of the kinetic energy at the bottom converted into an increase in gravitational potential energy at the instant it stops.
(a) What is the speed of the ball's center of mass at the base of the ramp?
(b) At this position, what is the speed of a point at the top of the ball?
(c) At this position, what is the speed of a point at the bottom of the ball?
(d) What maximum vertical height up the ramp does the ball move?