A rubber ball dropped on a hard surface takes a sequence of bounces, each one Four fifths 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?

Answer 1

To find the total vertical distance traveled by the ball when it hits the surface for its fifth bounce, we need to sum up the distances traveled during each bounce.

The height of the first bounce is 10 feet.
The height of the second bounce is (4/5) * 10 = 8 feet.
The height of the third bounce is (4/5)^2 * 10 = 6.4 feet.
The height of the fourth bounce is (4/5)^3 * 10 = 5.12 feet.
The height of the fifth bounce is (4/5)^4 * 10 = 4.096 feet.

To find the total vertical distance traveled by the ball when it hits the surface for its fifth bounce, we sum up the distances traveled during each bounce:

10 + 8 + 6.4 + 5.12 + 4.096 = 33.616 feet

Therefore, the total vertical distance traveled by the ball when it hits the surface for its fifth bounce is 33.616 feet.