Bouncing Ball.A ball dropped from a height of 39 feet bounces to 0.6666666667 of its former height with each bounce.Find the total vertical distance that the ball travels.
A) 195 feet
B) 82 feet
C) 234 feet
D) 111 feet
E) 117 feet

Question

​Bouncing Ball.A ball dropped from a height of 39 feet bounces to 0.6666666667 of its former height with each bounce.Find the total vertical distance that the ball travels. ​
A) ​195 feet
B) ​82 feet
C) ​234 feet
D) ​111 feet
E) ​117 feet

Quizplus · Accepted Answer

The total vertical distance traveled by the ball can be found using the formula for the sum of an infinite geometric series, $S = \frac{a}{1 - r}$, where $a$ is the first term and $r$ is the common ratio. Here, $a = 39$ feet (the initial drop) and $r = 0.6666666667$ (the bounce back ratio). The distance going up is the same as the distance going down for each bounce, so we need to double the series sum for the bounces, but not the first drop: $Total\ distance = a + 2(\frac{ar}{1 - r})$. Substituting the given values, $Total\ distance = 39 + 2(\frac{39 \times 0.6666666667}{1 - 0.6666666667}) = 39 + 156 = 195$ feet.

​Bouncing Ball

Bouncing Ball