Randall D. Knight — Impulse and Momentum: Problem 66

Consider a partially elastic collision in which ball A of mass \( m \) with initial velocity \( (v_{ix})_A \) collides with stationary ball B, also of mass \( m \), and in which \( 1/4 \) of the mechanical energy is dissipated as thermal energy. Find expressions for the final velocities of each ball. Hint: Mathematically there are two solutions; however, one of them is physically impossible.