Answer to Question #251691 in Algebra for Pear

Question

a ball is dropped from a height of 12 m. after each bounce it rises to 85% of its previous height.

a) determine the height of the ball after the 8th bounce

b) determine the total vertical distance the ball travels when it hits the ground for the 6th time

Answer 1

Solution

Given;

$h_1=12m$

The second height will be;

$h_2=0.85×12=10.2m$

$h_3=0.85×10.2=8.67m$

Clearly this is a form of geometric series in which;

The first term ,a=12m

The common ratio,r=0.85

(a)

The height after the 8th bounce.

From geometric series,the nth term is give as:

$n_{th}=ar^{n-1}$

$n_8=12×0.85^{8-1}=3.847m$

(b)

total distance after ball hit ground for the 6th time.

Summation of terms from geometric series is ;

$S_n=\frac{a(r^n-1)}{r-1}$

$S_6=\frac{12(0.85^6-1)}{0.85-1}$

$S_6=49.828m$