I vaguely recall a rule somewhere that elastic deformation cannot exceed the speed of sound, for reasons having to do with shockwave propagation or something like that.
Can’t exceed the speed of sound in the material, not speed of sound in the atmosphere.
But that nitpick probably doesn’t change your assertion that it’s not going to work.
Actually, the (vertical) velocity of the deflected center point of the rubber band is faster than the axial contraction of the rubber band itself (at that point) which is limited by the speed of sound of the material.
Derivation: Pythagoras, chain rule
Based on that, knowing the speed of sound of rubber, one can obtain a minimal required length of the rubber band.
Can’t exceed the speed of sound in the material, not speed of sound in the atmosphere.
But that nitpick probably doesn’t change your assertion that it’s not going to work.
I’ve added this clarification to my comment. Thanks!
It seems that common types of rubber have a propagation speed in the range of 1.5-1.8 km/s, so we’re still quite a bit away from 10.5 km/s.
Actually, the (vertical) velocity of the deflected center point of the rubber band is faster than the axial contraction of the rubber band itself (at that point) which is limited by the speed of sound of the material.
Derivation: Pythagoras, chain rule
Based on that, knowing the speed of sound of rubber, one can obtain a minimal required length of the rubber band.
Speed of sound in the air is a serious problem as well. It would probably break most rubber bands.