Imagine a ball dropped from a height of 40 meters. Each time it strikes the ground, it bounces 0.68 times as high as the previous bounce. Find the total distance the ball will travel if it is allowed to bounce indefinitely.
A) 27.2 meters
B) 0.32 meters
C) 210 meters
D) 40 meters

Question

Quizplus · Accepted Answer

Let's consider the distance traveled in each bounce. The first time the ball bounces it travels 40 meters (the height from which it was dropped) up and 40 meters down, a total distance of 80 meters. The second bounce will then travel 0.68*40 = 27.2 meters up and 27.2 meters down, a total distance of 54.4 meters. Similarly, the third bounce will travel 0.68^2*40 = 18.496 meters up and down, a total distance of 36.992 meters, and so on.

This creates a geometric series:

80 + 54.4 + 36.992 + ...

Using the formula for the sum of an infinite geometric series:

S = a/(1-r),

where a is the first term (80) and r is the common ratio (0.68).

S = 80/(1-0.68) = 250 meters

Therefore, the total distance traveled by the ball if it bounces indefinitely is 250 meters. The correct answer choice is C.

Imagine a Ball Dropped from a Height of 40 Meters