On an ideally smooth horizontal surface lies a rod of length l and mass m, which can slide along this surface without friction (figure). A ball of mass m, moving perpendicular to the rod, hits one of the points of the rod. At what distance x from the middle of the rod must the impact occur for the ball to transfer all its kinetic energy to the rod? The impact is considered to be absolutely elastic. At what ratio of masses M and m is this possible?

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