A ball is dropped from a height of 12m. On every successive bounce, the ball bounces to a height that is 2/3 of the previous height. Find the total vertical distance, that the ball has travelled when it hits the ground for the 8th time?

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Answer 1 · 2018-03-10T12:41:14

Total distance travelled by ball is #57.19# m.

The ball falls #12# m and rebounds #12*2/3=8# m , then falls

#8# m and rebounds #8*2/3=16/3# m and so on . The following

series gives the total distance travelled by the ball.

#F=12+(12*2/3)+(12*2/3*2/3)+.... 8#th term and

#R=8+(8*2/3)+(8*2/3*2/3)+.... 7#th term

G.P series sum formula: #S_n=(a(r^n-1))/(r-1)#.

For forward distance #a=12 , r=2/3, n=8#

#:. F={12((2/3)^8-1)}/(2/3-1)~~34.595# m

For rebound distance #a=8 , r=2/3, n=7#

#:. R={8((2/3)^7-1)}/(2/3-1)~~22.595# m

Total distance travelled by ball is #34.595+22.595~~57.19# m

Total distance travelled by ball is #57.19# m [Ans]