Bouncing Ball. A ball dropped from a height of 35 feet bounces to $1 / 2$ of its former height with each bounce. Find the total vertical distance that the ball travels.
A)105 feet
B)140 feet
C)64 feet
D)53 feet
E)70 feet

Question

Quizplus · Accepted Answer

The ball initially falls 35 feet. It then bounces up to $ \frac{1}{2} \times 35 = 17.5 $ feet and falls the same distance. This pattern continues, creating a geometric series for the upward and downward distances. The total distance is the sum of the initial drop and twice the sum of the infinite series of bounces: $ 35 + 2 \times (17.5 + 8.75 + 4.375 + \ldots) $. The series sum is $ \frac{17.5}{1 - 0.5} = 35 $. Thus, the total distance is $ 35 + 2 \times 35 = 105 $ feet.

Bouncing Ball 1/21 / 21/2 Of Its Former Height with Each Bounce

Bouncing Ball $1 / 2$ Of Its Former Height with Each Bounce