The bouncing ball

Mathematically, it does not come to rest.

59 2/3 meters

Wait. Dammit. That's only height....

65.6333333333333333333333333333333333333333333... meters

No idea how to display a repeating decimal.

It won't come to rest, but it's a convergent series.

Is there a mathematical formula to get to the answer, Drewdad, other than endlessly adding all the different fall and bouncing heights?

I'm sure there is; I know it was covered in one of my math classes.

Unfortunately, I haven't used it in 20 years or so.

Except for the first term, it's a geometric series:

53.7 + 2*(5.37/(1-0.1)

53.7 is the initial drop
(5.37/(1-.01)) is the sum of the remaining drops (geometric series)
2 is there because after the first drop, there is a rebound that is equal to the next drop.

D=53.7+2*(53.7*0.1+53.7*0.01+.......)=53.7[1+2(0.1+0.01+......)]=53.7[1+2*0.1∑0.1^n]=53.7[1+2*0.1(1/(1-o.1))]=53.7[1+0.2/0.9]=53.7(11/9)=65.63333333 m

Rap

Thanks Mark and Raprap, that was helpful.