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? (1 point)
28 77/125 feet
49 1/25 feet
57 29/125 feet
59 29/125 feet
57 29/125 feet
The total vertical distance traveled can be calculated as follows:
10 + 10(4/5) + 10(4/5)^2 + 10(4/5)^3 + 10(4/5)^4
10 + 8 + 6.4 + 5.12 + 4.096 = 33.616
Therefore, the total vertical distance is 33.616 feet, which is equivalent to 57 29/125 feet.