A rubber ball dropped on a hard surface takes a sequence of bounces, each one 4/5 as high as the preceding one. If this
ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled at the time when it hits the
surface for its fifth bounce?
28 77/125 feet
49 1/25 feet
57 29/125 feet
59 29/125 feet
To find the total vertical distance traveled by the ball up to the fifth bounce, we can first calculate the distance traveled during each bounce, and then add them up.
First bounce: 10 feet
Second bounce: 10 * 4/5 = 8 feet
Third bounce: 8 * 4/5 = 6.4 feet
Fourth bounce: 6.4 * 4/5 = 5.12 feet
Fifth bounce: 5.12 * 4/5 = 4.096 feet
Adding all these distances together:
10 + 8 + 6.4 + 5.12 + 4.096 = 33.616 feet
So, the total vertical distance the ball has traveled at the time of its fifth bounce is 33.616 feet.
Therefore, the answer is 33 133/125 feet.