Question

A ball is dropped from a height of 8 feet. If every time it bounces, it bounces 60% of its previous height, what is the total distance traveled by the ball?

Answer 1

Answer:

20feet

Step-by-step explanation:

Initial height of the ball = 8feet

If it bounces 60% of its previous height, its new height will be;

60% of 8

= 60/100 * 8

= 480/100

= 4.8 ft

If it bounces 60% of its current distance, new height will be expressed as;

60% of 4.8

= 0.6 * 4.8

= 2.88

The height of the ball will keep reducing and form a geometric progression of the form 8, 4.8, 2.88...

In order to get the total distance traveled by the ball, we need to calculate the sum to infinity of the sequence;

S∞ = a/1-r where;

a is the first term = 8

r is the common ratio

$r = \frac{4.8}{8} = \frac{2.88}{4.8}\\r = 0.6$

Substitute into the formula;

S∞ = a/1-r

S∞ = 8/1-0.6

S∞ = 8/0.4

S∞ = 20feet

Hence the total distance traveled by the ball is 20feet