Can't catch the ball

Adventurous Mary tries a new game: she puts on her rollerblades and throws the ball towards the wall, lets it bounce off, catches it again, throws it right back, and so on. She notices a strange thing: after the second throw, she is unable to catch the ball anymore since the ball never reaches her. What is the maximum ratio of Mary's mass to the ball's mass in order for this to happen?

Details and assumptions

  • There is no friction between the rollerblades and the surface, and Mary can slide freely.
  • Mary's first throw is from the rest.
  • The ball bounces elastically from the wall.
  • Mary throws the ball such that it always has the same speed with respect to the ground.
  • Neglect any gravitational influences.

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