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

5256 views around the world

You can reuse this answer
Creative Commons License

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

[Ans]