Aball 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.

42 feet

Step-by-step explanation:

so when the ball hit the ground for the 1st time it travels a distance of 6 feet.

for later bounces let Di be the distance traveled  up and down.

D1= 6 feet

D2 and D3 would be

similarly D3 is

by repeating this process we can find the vertical distance traveled by the ball

=6+12∑

where n=0,1,2,.....∞

=6+12(3/4)∑

this is answer of 144 cubic meters