Question
A ball is dropped from a height of 2 metres and bounces
height on each bounce.
(1) When it hits the ground for the
(2) How high off the floor is the ball after the
height on each bounce.
(1) When it hits the ground for the
(2) How high off the floor is the ball after the
Ask by Munoz Norton. in South Africa
Dec 21,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
After the 8th bounce, the ball has traveled approximately 8.322 meters and is about 0.336 meters above the floor.
Solution
Let’s analyze the problem step by step.
Given:
- Initial height (
) = 2 meters - Each bounce reaches
of the previous height.
Mathematically, the height after the
1. Total Distance Traveled by the
When the ball hits the ground for the
The total distance (
Where:
This is a geometric series where:
Thus:
2. Height After the
After the
Final Answers:
- Total distance traveled by the
hit: Approximately 8.322 meters. - Height after the
bounce: Approximately 0.336 meters.
Answer:
- After the eighth ground hit, the ball has traveled approximately 8.322 meters;
- Its height above the floor following the eighth bounce is approximately 0.336 meters.
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Explain 
Simplify this solution Extra Insights
(1) To find the total distance the ball has traveled after hitting the ground for the
- First drop:
m (down) - First bounce:
m (up and down) - Second bounce:
m (up and down) - Third bounce:
m (up and down)
Continuing this pattern…
We can express the distances travelled after each bounce as:
The summation is a geometric series where:
- First term
- Ratio
- Number of terms
The sum formula is:
Thus, calculating the total distance:
After plugging in the numbers and calculating, the total distance traveled by the ball after hitting the ground for the
(2) To find the height of the ball after the
For the initial height
Calculating this gives:
So, after the
