Classic Rotational Motion Problem

Classical Mechanics Level 4

A Solid sphere is rolling purely on a rough horizontal surface ( Coefficient of kinetic friction = μ) with speed of centre = V. It collides inelastically with a smooth vertical wall at a certain moment, the coefficient of restitution being $\frac{1}{2}$ . The sphere will begin pure rolling after a particular time which can be expressed in form of $\frac{aV}{bμg}$ where a and b are co-prime.

Classic Rotational Motion Problem

Find a + b.