Problem 1.176

Three identical $\operatorname{discs} A, B,$ and $C$ (Fig. 1.45 ) rest on a smooth horizontal plane. The disc $A$ is set in motion with velocity $\mathbf{v}$ after which it experiences an elastic collision simultaneously with the discs $B$ and $C .$ The distance between the centres of the latter discs prior to the collision is $\eta$ times greater than the diameter of each disc. Find the velocity of the disc $A$ after the collision. At what value of $\eta$ will the disc $A$ recoil after the collision; stop; move on?