a tennis ball dropped from a height of 30m bounces 40% of the height from which it fell on each bounce. what is the vertical distance it travels before coming to rest?

Answer 1

first bounce = 30 m
2nd bounce = 2(.4)(30) = 60(.4) , up and down
3rd bounce = 2(.4)^2 (30)= 60(.4)^2
..
nth bounce = 60(.4)^(n-1)

total distance
= 30 + (60(.4) + 60(.4^2) + 60(.4^3) + .... )

So consider it to be an infinite geometric series starting with the second bounce
a = 60(.4)
r = .4
sum ∞ = a/(1-r)
=60(.4)/.6 = 40
but we can't forget the initial drop from 30 m

so total distance = 70 m

Answer 2

A vacuum pump remove 25% to the air from a scaled jar on each strike of its piston.The jar contains one litre of air before the pump starts.write a sequence to the amount of air remaining inside the jar after each stroke of the piston.will there ever be no air inside the jar?.