There and back again

Suppose you want to throw a super ball so that it bounces back and forth, retracing the same trajectory, as shown above. If you throw the ball horizontally with velocity 1 m/s,\SI[per-mode=symbol]{1}{\meter\per\second}, what spin ω\omega (in rad/s\si[per-mode=symbol]{\radian\per\second}) must you give it so that it does what you want?

Assumptions and Details

  • The collision with the ground is perfectly elastic.
  • The ball does not slip while it contacts the ground.
  • The radius of the ball is 3 cm.\SI{3}{\centi\meter}.

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