Arturo O. answered • 12/23/17

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You can figure this out by iteration. Start with initial drop from a height H.

Bounce 1:

H → H

_{1}= H/2Bounce 2:

H

_{1 }→ H_{2}= H_{1}/2 = H/2^{2}Bounce 3:

H

_{2}→ H_{3}= H_{2}/2 = H/2^{3}Do you see the pattern here?

Bounce k:

H

_{k}→ H_{k-1}/2 = H/2^{k}If it reached 1/8 of its initial potential energy, then it reached H/8 of its initial height.

H/8 = H/2

^{n}8 = 2

^{n}**n = 3**