math
posted by Melissa .
a ball is dropped from a height of 3m and bounces on the ground . At the top of each bounce, the ball eaches 60% of its previous height. Calculate the total distance travelled by the ball when it hits the ground for the fifth time

This is just finding the sum of the sum of the series
3 + 6*.6 + 6*.6*.6 + ...
We subtract off the 3 because the ball didn't start from the ground, so its first hop is only the downward part.
a = 6
r = 0.6
S5 = 6 (1.6^5)/(1.6)
= 6(2.3056) = 13.8336
S5  3 = 10.8336
Check: 3 + 3.6 + 2.16 + 1.296 + 0.7776 = 10.8336 
a ball is droped from a height of 30m above level ground. After each bounce it rises to three quarters of the height from which it fell. find,to the nearest metre, the total distance it has travelled when it strikes the ground for the 7th times

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