A ball is dropped from a height of 12 feet and returns to a height that is half the height from which it fell. the ball continues to bounce half the height of its previous bounce each time. How far will the ball have traveled vertically when it hits the ground for the fourth time?
24 feet, 33 feet, 12 feet, or 3 feet?
Can someone explain this for me?
33 ft
Add up every time it travels both up and down.
12 + 6 + 6 + 3 + 3 + 1.5 + 1.5 = 33
To determine how far the ball will have traveled vertically when it hits the ground for the fourth time, we need to calculate the total vertical distance covered by the ball.
Initially, the ball is dropped from a height of 12 feet. It then bounces back up to a height that is half of its previous bounce, which is 12/2 = 6 feet. This is the first bounce.
For the second bounce, the ball falls from 6 feet and bounces back up to half that height, which is 6/2 = 3 feet.
For the third bounce, the ball falls from 3 feet and bounces back up to half that height, which is 3/2 = 1.5 feet.
Finally, for the fourth bounce, the ball falls from 1.5 feet and bounces back up to half that height, which is 1.5/2 = 0.75 feet.
To find the total vertical distance traveled, we add up the heights of the drops and the bounces:
12 + 6 + 3 + 1.5 + 0.75 = 23.25 feet
Therefore, the ball will have traveled vertically a total distance of approximately 23.25 feet when it hits the ground for the fourth time. So, the closest option to this answer is 24 feet.
To find out how far the ball will have traveled vertically when it hits the ground for the fourth time, we need to calculate the total vertical distance traveled by the ball.
First, let's break down the motion of the ball. The ball is dropped from a height of 12 feet. After the first bounce, it reaches a height that is half the height from which it fell, which is 12/2 = 6 feet. For each subsequent bounce, the ball reaches a height that is half the height of the previous bounce.
We can calculate the total distance traveled by summing up the heights reached during each bounce.
Bounce 1: 12 feet (dropped from)
Bounce 2: 6 feet
Bounce 3: 3 feet
Bounce 4: 1.5 feet
Now, let's add up these heights to get the total vertical distance traveled.
12 + 6 + 3 + 1.5 = 22.5 feet
Therefore, the ball will have traveled a total vertical distance of 22.5 feet when it hits the ground for the fourth time.
So, the closest answer choice is 24 feet.