Bouncing with Friction

Can we determine the range of a projectile that bounces with both a coefficient of restitution and a coefficient of friction? And can we maximize that range? Previous projectile-with-friction video: https://youtu.be/YBROfaGFVKc 0:00 - Introduction 1:40 - The impulse-momentum theorem 5:06 - Updating the velocity components 9:21 - A recursion relation 11:20 - Solving the recurrence 14:59 - Finding the range 23:01 - Maximizing the range 28:32 - Summary of results and conditions on bounce angle 33:35 - Simulation code 37:02 - Conclusion Cf. "Solved Problems in Classical Mechanics" #6.5 Also https://physics.stackexchange.com/questions/1142/is-there-a-2d-generalization-of-the-coefficient-of-restitution HW: Find the total time in flight. What if the projectile is a sphere with moment of inertia _I=βmr^2_? You'll need to account for angular impulse delivered in a bounce.