Bouncing ball

[bactomac]

A ball is dropped from a height of 1 metre and always bounces to two thirds of its previous height. How far does it travel altogether?

[spitza]

2 and 1 thirds I think

[Rollo]

5 metres

[swannbaker]

Infinity .

[Rollo]

Yes, infinity in theory, but in practice the total distance travelled tends to a limit of 5 metres.

[factor-fiction]

No, 3 metres

[factor-fiction]

Sorry, i only counted the downward bits. Will recalculate

[factor-fiction]

Yes answer is 5 metres. Here is some working if you need it.

1+2(⅔) +2 (⅔)� +(⅔)�+....
=2(1+(⅔) + (⅔)� +(⅔)�+...) -1
=[2/ (1-⅔)] * -1
=6-1
=5 (metres)

(* uses result that sum of geometric series with ratio of r (in this case ⅔) is 1/(1-r), (which in this case is 1/(1-⅔) = 1/(⅓) =3