# 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 $$\SI[per-mode=symbol]{1}{\meter\per\second},$$ what spin $$\omega$$ (in $$\si[per-mode=symbol]{\radian\per\second}$$) 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 $$\SI{3}{\centi\meter}.$$
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