# math

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A rubber ball is dropped from a height of 729 feet, and at each bounce it rebounds one-third of the height from which it last fell. How far has the ball travelled by the time it strikes the ground for the 5th time?

• math -

first time: 729/3=243
second time: 243/3
third time:81/3
fourth time: 27/3
fifth time: 9/3=3ft

• math -

distance for 1st bounce = 729
distance for 2nd bounce = 2(1/3)(729) = 2(243)
distance for 3rd bounce = 2(1/3)(243) = 2(81)
distance for 4th bounce = 2(1/3)(81) = 2(27)
distance for 5th bounce = 2(1/3)(27) = 2(9)

total distance
= 729 + 2(243+81+27+9) = 1449

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