1. A rubber ball
is dropped from a height of 15 meters. On each rebound, it rises 2/3 of the
height from which it last fell. Find the distance traversed by the ball before
it comes to rest. The geometric progression occurs after the first rebound.
A. 96 m
B. 85 m
C. 100 m
D. 75 m
Solution:
It is an infinite geometric series problem that starts
after the first rebound. The Formula used is:
Where:
S = sum of the geometric progression
a = starting number
r = common ratio
The result is multiplied by 2 since the
ball must travel upwards and downwards.
And finally, the initial drop of the
ball, which is 15 meters is added to the result which gives: