The distance travelled in (m) by a ball dropped from a height are 128/9,32/3,8,6, ...

How much distance will it travel before coming to rest

Answer: it will trave 56.89 meters before coming to rest.

Step-by-step explanation:

This is a geometric progression since the distance travelled (height) by the ball is reducing by a constant ratio, r. Since the number of times that the ball will bounce is infinite, then we would apply the formula for determining the sum of the terms in a geometric progression to infinity which is expressed as

S = a / (1 - r)

where

S = sum of the distance travelled by the ball

a = initial distance or height of the ball

r = common ratio

From the information given,

a = 128/9

r = (32/3) / (128/9) = 0.75

Therefore,

S = (128/9) / (1 - 0.75) = 56.89 meters