Solving a problem in physics section 31 point 57 mecha

Solving a problem in physics section 31 point 57 mecha

57. On a perfectly smooth horizontal surface is the rod length l and mass M. In one of the points of the rod hits the ball of mass m, moving on the surface perpendicular to the shaft. Assuming an elastic blow completely determine at what distance x from the middle of the rod should happen kick the ball passed the rod to all its kinetic energy? At what ratio of the mass M and m is this possible?

Additional information:

Detailed solution. Decorated in Microsoft Word 2003. (Target decided to use formula editor)