The bouncing ball

Reply Tue 21 Feb, 2012 04:18 am
A small rubber ball falls from a tower (height 53.70 metres). Everytime the ball hits the ground, it bounces back up one tenth of the length of its fall. What distance does the small ball cover before it comes to rest on the ground?
  • Topic Stats
  • Top Replies
  • Link to this Topic
Type: Question • Score: 1 • Views: 6,587 • Replies: 7
No top replies

Reply Tue 21 Feb, 2012 07:03 am
Mathematically, it does not come to rest.
0 Replies
Reply Tue 21 Feb, 2012 08:24 am
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.

Reply Wed 22 Feb, 2012 03:55 am
Is there a mathematical formula to get to the answer, Drewdad, other than endlessly adding all the different fall and bouncing heights?
Reply Wed 22 Feb, 2012 08:31 am
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.

0 Replies
Reply Wed 22 Feb, 2012 09:47 am
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.

Reply Sat 25 Feb, 2012 01:28 pm
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

0 Replies
Reply Thu 1 Mar, 2012 04:14 pm
Thanks Mark and Raprap, that was helpful.
0 Replies

Related Topics

Amount of Time - Question by Randy Dandy
logical number sequence riddle - Question by feather
Calc help needed - Question by mjborowsky
HELP! The Product and Quotient Rules - Question by charsha
STRAIGHT LINES - Question by iqrasarguru
Possible Proof of the ABC Conjecture - Discussion by oralloy
Help with a simple math problem? - Question by Anonymous1234567890
How do I do this on a ti 84 calculator? - Question by Anonymous1234567890
  1. Forums
  2. » The bouncing ball
Copyright © 2024 MadLab, LLC :: Terms of Service :: Privacy Policy :: Page generated in 0.03 seconds on 06/24/2024 at 07:21:00