Question

a rubber ball has the property that on any bounce it returns to 1/3 of the height from which it just fell. Suppose the ball is dropped from 108 ft How far has the ball traveled by the fourth bounce?

Answer 1

end of first bounce it dropped 108 ft
during the second bounce it went up and down
(1/3) of 108 or 2(1/3)(108) = 72
during the third bounce it went
2(1/3)(72) = 48
during the fourth bounce it went
2(1/3)(48) = 32

so after 4 bounces it went
108+72+48+32 = 260

make a sketch, label the bounces and see why I only took half of the first bounce cylcle