How far does the golf ball travel before coming to rest?
Posted on
May 1st, 2010
by admin
A golf ball is dropped from a height of 81 inches. It rebounds to 2/3 of its original height and continues rebounding in this manner. How far does it travel before coming to rest?
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sv ,
EDIT: (and Rocky, too)…
have given you a wonderful solution to your geometric series question. The other answers are so much "hand waving" junk. Those folks have no idea what is going on in the problem…forget their prattle!!
There are many examples of infinite processes that have finite results. This is one example.
The old joke: A man closes the distance between himself and his beautiful wife by 1/2 each time he moves. The ignorant say "He never reaches her." He answers "I get close enough."
-Fred
thoereticaly speaking it never come to a rest (assuming it bounces exatly 2/3 its last bounce every time, scince you can divide any number (no matter how small).)
it travelled = 81[1 + 2{2/3 + (2/3)^2 + ...}] in
= 81[1 + 2{2/3 / (1 --2/3)}] in
= 405 inches
depends what you call rest, this is how it goes
1st bounce = 2/3rds of 81 = 54
2nd bounce = 2/3rds of 54 =36
3rd bounce = 2/3rds of 36 = 24
4th …blah blah blah = 16
5th = 10
6th = 6.66
7th 4.4
and it carries on for a long time