Suppose a ball is dropped from a height of 16 feet.Each time it drops h feet, it rebounds 0.85h feet.Find the total distance traveled by the ball.Round your answer to two decimal
Places.
A)229.33 feet
B)410.67 feet
C)181.33 feet
D)197.33 feet
E)213.33 feet

Question

Quizplus · Accepted Answer

The total distance traveled by the ball can be found by adding the distance it travels during each drop and rebound. 
On the first drop, the ball travels 16 feet. On the first rebound, it travels 0.85(16) = 13.6 feet. On the second drop, it travels another 13.6 feet, and on the second rebound, it travels 0.85(13.6) = 11.56 feet.

This pattern continues, so we can set up a geometric sequence:

a1 = 16 (the initial drop) 
r = 0.85 (the rebound factor)

The total distance traveled will be:

16 + 2(0.85)(16) + 2(0.85)^2(16) + 2(0.85)^3(16) + ...

Using the formula for the sum of an infinite geometric series, we get:

a1 / (1 - r) = 16 / (1 - 0.85) = 106.67

However, the ball does not travel an infinite distance - it stops bouncing once it reaches the ground. The last distance it travels is the distance of the last rebound, which can be found by multiplying the distance of the previous rebound by the rebound factor:

0.85^6(16) ≈ 4.69

So the total distance traveled by the ball is approximately 16 + 2(0.85)(16) + ... + 4.69, which is approximately 197.33 feet. Therefore, the best choice is D.

Suppose a Ball Is Dropped from a Height of 16