IPT2020-Problem 14- Jumping bean (National and Kapodistrian University of Athens, Greece)

IPT2020 Problem 14 Jumping bean: A simple toy called a "jumping bean" can be constructed by putting a metal ball inside of a pill capsule. Placed on an inclined surface at a certain inclination, the jumping bean will tumble down in a rather surprising way, seemingly standing up-right, flipping end to end, instead of rolling. Investigate its motion. Find the dimensions of the fastest and slowest beans for a given inclination