A rubber ball dropped on a hard surface takes a sequence of bounces, each one two-fifthsas 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)
Responses
22 start fraction 12 over 25 end fraction feet
22 Image with alt text: start fraction 12 over 25 end fraction feet
32 Start Fraction 124 over 125 End Fraction feet
32 Image with alt text: Start Fraction 124 over 125 End Fraction feet
25 Start Fraction 124 over 125 End Fraction feet
25 Image with alt text: Start Fraction 124 over 125 End Fraction feet
22 Start Fraction 124 over 125 End Fraction feet
The total vertical distance traveled at the time of the fifth bounce can be calculated as follows:
10 + (2/5) * 10 + (2/5)^2 * 10 + (2/5)^3 * 10 + (2/5)^4 * 10
= 10 + 4 + 1.6 + 0.64 + 0.256
= 16.9 feet
Therefore, the total vertical distance traveled at the time of the fifth bounce is 16.9 feet.
Correct Answer: 22 12/25 feet