A steel ball was dropped from a height of 81 and rebounded , on each bounce,Two thirds of he distance from which it fell.How far it travel before coming to rest.?

Question

Infinite Geometric sequence

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Answer 1 · 2018-08-01T12:52:34

Total distance traveled is $405$ unit.

Sum of infinite geometric series is $S=a_1/(1-r) ; |r| <1$

$a_1=81 and r= 2/3$ are first term and common ratio.

The geometric series for falls are $81 , 54 , 36 ,24 ......$

Sum of distances covered during falls $S_F=81/(1-2/3)$ or

$S_F= 81/(1/3)=243$ unit

The geometric series for rebounds are $54 , 36 ,24,16 ......$

Sum of distances covered during rebounds $S_R=54/(1-2/3)$ or

$S_R= 54/(1/3)=162$ unit.

Total distance traveled is $S= S_F+S_R= 243+162= 405$ unit

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