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]