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If yes, what physics concepts make this possible? This isn't for any class or anything, is just a honest doubt of mine.

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Yes it can. Glass is an elastic material (it just breaks at small deformations), and just like any other elastic material it can store energy like a spring. So you can have a situation like the one BowlOfRed pointed out, where by means of the shape of the cup and the way it impacts with the ground, you may end up with a piece of glass with a high velocity after the impact, enough to surpass the initial high (of course the total kinetic energy of this tiny piece of glass is lower than the initial potential energy of the whole cup). You may have the case of a tempered glass cup, where you got a lot of this potential elastic energy already stored in the material as a result of a heat treatment to the cup. As the glass breaks, this energy is released and it may push a piece of glass higher than its original position.

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