Answer: 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 :-
[tex]6\times\dfrac{7}{10}[/tex]
After 2nd bounce the height reached by the ball is given by :-
[tex]6\times\dfrac{7}{10}\times\dfrac{7}{10}=6\times(\dfrac{7}{10})^2[/tex]
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 ;-
[tex]\dfrac{a(1-r^n)}{1-r}[/tex]
Now, the total distance the ball bounces (distance falling and going up) through the 5th bounce is given by:-
[tex]\dfrac{6(1-(0.7)^5)}{1-0.7}=16.6386[/tex]
