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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