a rubber ball is dropped on the floor from a height of 27 M always requires one third of the distance of previous for find the distance it will have travelled before hitting the ground for the ninth time
Answers
HELLO EVERYONE!
The answer of this question is 53.9958 meters.
Let’s see how!
27 m distance is traveled by the ball once during fall, remaining all the distance 1/3 of the previous fall are traveled twice during fall and rebound so;
we have following series;
=27+2 (9+3+1+1/3+1/9+1/27+1/81+1/243)
=27+2(geometric series with a=9, r=1/3, n=8, l=1/243)
we have Sn =a-rl/1-r
where;
“Sn” is the sum of “n” number of terms,
“a” is the first term,
“r” is the common ratio,
“l” is the last term of the series.
by putting the values in this formula we get;
=27+2((9–1/3)∗(1/243))/1–1/3
=27+2(9–1/729)/2/3
=27+2∗3/2(6561–1/729)
=27+3(6560/729)
=27+6560/243
=6561+6560/243
=13121/243
=53.9m
So, the rubber ball have covered 53.9 m distance before hitting the ground for the ninth time!