2-28. Before a direct collision, two balls are moving toward each other with normally distributed velocities  and . The coefficient of restitution between the balls is . If the masses of the two balls are  and , respectively, determine the velocity distributions of the two balls just after the collision. Assume  and  are independent.

 

                                                                                

                                                                                                                    

Solving (1) and (2) yields

 

 

 

Therefore, ; .