A ball is dropped from a height of 6 feet and begins bouncing. the height of each bounce is three-fourths the height of the previous bounce. find the total vertical distance travelled by the ball.

Given:

ball is dropped from a height of 6 feet.

each bounce has a height of 3/4 the height of the previous bounce.

1st bounce: 6 x 3/4 = 4.5 feet

2nd bounce: 4.5 x 3/4 = 3.375 feet

3rd bounce: 3.375 x 3/4 = 2.531

4th bounce: 2.531 x 3/4 = 1.898

5th bounce: 1.898 x 3/4 = 1.424

The equation for the height of the bounce is:

3/4 = 0.75

h (n) = 6 (0.75) ^n; where n is the number of the bounce.

Total vertical distance traveled by the ball means the up and down the ball traveled. So, we add up the computed distance and multiply it by 2.

4.5 + 3.375 + 2.531 + 1.898 + 1.424 = 13.728

13.728 x 2 = 27.456 feet

The ball had a total vertical distance of 27.456 feet after bouncing 5 times.