an elastic ball rebounces 70% when it is dropped from the height. if it is dropped from 60m what is the total distance travelled by the ball
60+.7*60(2)+.7^2(60)*2+...
Sum from n=0 to large [2*60*.7^n) -60
sum 120*.7^n -60
geometric ratio,
= 120/(1-.7) - 60
= 120/.3 -60
=400-60=340
To find the total distance traveled by the ball, we need to calculate the sum of the distances traveled during each bounce.
The ball rebounces 70% of its previous height, meaning it reaches 70% of its previous height after each bounce.
Here's how you can calculate the total distance traveled:
1. Initial drop: The ball is dropped from a height of 60 meters, so the first distance traveled is 60 meters.
2. First bounce: After the first bounce, the ball reaches a height of 60 * 0.7 = 42 meters. It then falls back down to the ground, covering another 42 meters. So the total distance traveled after the first bounce is 42 + 42 = 84 meters.
3. Second bounce: After the second bounce, the ball reaches a height of 42 * 0.7 = 29.4 meters. It then falls back down to the ground, covering another 29.4 meters. So the total distance traveled after the second bounce is 29.4 + 29.4 = 58.8 meters.
4. We continue this process until the ball's height becomes negligible (essentially zero).
To calculate the total distance traveled, we need to find the sum of the distances traveled after each bounce. In this case, we can see a pattern emerging with the distances traveled: 60, 84, 58.8, ...
To find the total distance, we can sum an infinite geometric series with the first term of 60 and a common ratio of 0.7.
The formula to calculate the sum of an infinite geometric series is:
sum = a / (1 - r)
where:
- a is the first term (initial drop distance)
- r is the common ratio (rebounce percentage in decimal form)
Plugging in the values, we have:
sum = 60 / (1 - 0.7)
sum = 60 / 0.3
sum = 200
Therefore, the total distance traveled by the ball is 200 meters.