Suppose a ball is dropped from a height of 6 ft. it bounces back up. but each time it bounces, it reaches only 7/10 of its previous height. what is the total distance the ball bounces (distance falling and going up) through the 5th bounce?

16.6386 ft.

Step-by-step explanation:

Given: A a ball is dropped from a height of 6 ft.

Each time it bounces, it reaches only 7/10 of its previous height.

i.e. after 1st bounce the height reached by the ball is given by :-

After 2nd bounce the height reached by the ball is given by :-

Thus, it is following a geometric progression with common ratio (r)=7/10=0.7 and the first term = 6

The sum of geometric progression  of first n terms is given by ;-

Now, the  total distance the ball bounces (distance falling and going up) through the 5th bounce is given by:-

2x3 – 6x2 – 14x + 24 square centimeters

if i'm wrong i'm sorry : )