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# The bouncing ball

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?
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Type: Question • Score: 1 • Views: 6,587 • Replies: 7
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fresco

1
Tue 21 Feb, 2012 07:03 am
@whimsical,
Mathematically, it does not come to rest.
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1
Tue 21 Feb, 2012 08:24 am
@whimsical,
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.

whimsical

1
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?

1
Wed 22 Feb, 2012 08:31 am
@whimsical,
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.

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markr

1
Wed 22 Feb, 2012 09:47 am
@whimsical,
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.

raprap

1
Sat 25 Feb, 2012 01:28 pm
@whimsical,
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
0 Replies

whimsical

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

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