if a basketball is dropped from 160 feet, what is the total vertical distance the ball will travel from the moment it is dropped to the time it hits the floor for the fifth time?
LOL this is a perfect basketball and a perfect floor so all collisions are elastic and it bounce back up to 160 ft every time?
Four round trips and a fall so
9 * 160
To find the total vertical distance the ball will travel from the moment it is dropped to the time it hits the floor for the fifth time, we need to first find the distance the ball travels each time it hits the floor.
The distance traveled by the ball each time it hits the floor can be calculated using the formula for the distance traveled by an object in free fall:
d = (1/2) * g * t^2
Where:
- d is the distance traveled
- g is the acceleration due to gravity (32.2 feet per second squared)
- t is the time it takes for the ball to hit the floor
We can then calculate the time it takes for the ball to hit the floor for each bounce using the following formula:
t = sqrt((2 * d) / g)
Given that the ball is dropped from a height of 160 feet, we can calculate the total vertical distance traveled by adding up the distances traveled during each bounce. The ball will hit the floor a total of 5 times, so we will calculate the distance for each bounce and sum them up.
Let's calculate the total vertical distance traveled:
1. First bounce:
The ball is dropped from a height of 160 feet, so the distance traveled for the first bounce is:
d1 = (1/2) * g * t1^2
= (1/2) * 32.2 * sqrt((2 * 160) / 32.2)^2
2. Second bounce:
The ball will rebound to a height of half the initial drop height (80 feet). So the distance traveled during the second bounce is:
d2 = 2 * (1/2) * g * t2^2
= 2 * (1/2) * 32.2 * sqrt((2 * 80) / 32.2)^2
3. Third bounce:
Similarly, the distance traveled during the third bounce is:
d3 = 2 * (1/2) * g * t3^2
= 2 * (1/2) * 32.2 * sqrt((2 * 40) / 32.2)^2
4. Fourth bounce:
The distance traveled during the fourth bounce is:
d4 = 2 * (1/2) * g * t4^2
= 2 * (1/2) * 32.2 * sqrt((2 * 20) / 32.2)^2
5. Fifth bounce:
Finally, the distance traveled during the fifth bounce is:
d5 = 2 * (1/2) * g * t5^2
= 2 * (1/2) * 32.2 * sqrt((2 * 10) / 32.2)^2
Now, we can calculate the total vertical distance traveled by summing up all the distances:
Total distance = d1 + d2 + d3 + d4 + d5
Compute the values of d1, d2, d3, d4, d5 using the formulas provided, and calculate the sum to find the total vertical distance traveled by the ball.