Question

Prc

Problem of the
Week Fourteen
I
Instructions...
A basketball is shot for the hoop and misses. A foul is called, and all the basketball
up vertically 2/3 of the way it fell, and then falls again. The process continues with the
players stop play. The ball drops 10 feet vertically to the court surface. It bounces back
ball bouncing vertically up and down until the basketball comes to rest.
Name Sidny Moore
Period
What is the total distance travelled by the
basketball?
d = IDFF
Upward di = 2/3

Answer 1

The total distance travelled by the basketball is 40 feet, which includes the initial fall distance and the subsequent rise and fall distances after each bounce.

Step-by-step explanation:

To find the total distance travelled by the basketball, we need to consider the distance it falls and the distance it rises after each bounce. The basketball initially falls 10 feet vertically to the court surface. Then, it bounces back up vertically 2/3 of the way it fell. This process continues until the basketball comes to rest. To calculate the total distance, we can use the formula:

Total distance = initial fall distance + sum of all subsequent rise and fall distances

Let's calculate the total distance:

1. Initial fall distance = 10 feet
2. Rise and fall distances = 2/3 * 10 + 2/3 * (2/3 * 10) + 2/3 * (2/3)^2 * 10 + ...
3. We can see that this is a geometric series with a common ratio of 2/3 and an initial term of 10
4. Using the formula for the sum of an infinite geometric series, we get:
5. Rise and fall distances = 10 / (1 - 2/3) = 10 / (1/3) = 30 feet
6. Total distance = initial fall distance + rise and fall distances = 10 + 30 = 40 feet

Therefore, the total distance travelled by the basketball is 40 feet.