A ball is dropped from a height of 12m and it rebounds ½ of the distance it falls. If continues to fall and rebound in this way, how far will it travel before comming to rest?
Answers
Given,
A ball is dropped from a height of 12m and it rebounds ½
When it rebounds first time,
It travles 12 m and rebounds 12/2 = 6 m,
Distance covered = 12 +6
When it rebounds second time,
It travles 6 m and rebounds 6/2 = 3 m,
Distance covered = 6 + 3
And so on................. upto infinity terms!
Hence,
Total Distance Covered = 12 + 6 + 6 + 3 + 3 + ................ ∞
= 12 + (6 + 3 + ...........∞)
= 12 + 2{6/(1 - 1/2)}
= 12 + 2*12
= 12 + 24
= 36 m
Note:- Sum of infinite terms of G.P. = a/1-r
Where a = first terms of G.P.
r = common ratio between terms
