Solve the problem.
-Mari drops a ball from a height of 22 meters and notices that on each bounce the ball returns to about $\frac { 7 } { 8 }$ of its previous height. About how far will ball travel before it comes to rest?
A) 176 m
B) 330 m
C) 352 m
D) 47.1 m

Question

Quizplus · Accepted Answer

We can use geometric series to solve the problem. Let the distance the ball travels before coming to rest be denoted by S. Then, the ball initially drops from a height of 22 meters, so the distance traveled after the first bounce is 22+22(7/8). After the second bounce, the distance traveled is 22+22(7/8)+22(7/8)^2. In general, after the nth bounce, the distance traveled is 22+22(7/8)+22(7/8)^2+...+22(7/8)^(n-1).

We want to find S, which is the sum of this infinite series. Using the formula for the sum of an infinite geometric series, we have:

S = 22/(1-7/8) = 22/1/8 = 176

Therefore, the ball will travel a total of 176 meters before coming to rest.

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