A table tennis ball is dropped from a height of 5ft. The ball rebounds to 60% of its previous height after each bounce.
Write an infinite geometric series to represent the distance that the ball travels after it initially hits the ground. (hint, the ball travels up and down on each bounce).
please help fast
After it initially hits the ground, the ball will travel
2(5)(.6) + 2(5)(.6)^2 + 2(5)(.6^3) + ....
= 10( .6 + .6^2 + .6^3 + .... )
or
= 6 + 6(.6) + 6(.6^2) + ...
a = 6, r = .6 , sum∞ = a/(1-r) = 6/.4 = 15
Sure, I can help you with that.
To write an infinite geometric series that represents the distance the ball travels after it initially hits the ground, we need to consider the distances covered during each bounce.
Let's break down the problem step by step:
1. The first thing we need to do is determine the distance the ball travels during the first bounce. Since the ball is dropped from a height of 5ft and rebounds to 60% of its previous height, the distance covered during the first bounce is 5ft + 60% of 5ft.
2. Now, let's calculate the distance covered during the second bounce. Since the ball rebounds to 60% of its previous height, the distance covered during the second bounce would be 60% of the distance covered during the first bounce.
3. Following the same pattern, the distance covered during the third bounce would be 60% of the distance covered during the second bounce.
And so on...
Based on this pattern, we can see that each term in the infinite geometric series is a 60% reduction of the previous term.
Now, let's write the infinite geometric series:
First term = 5ft + 60% of 5ft
Common ratio = 60% or 0.6
The infinite geometric series can be written as:
S = 5ft + (5ft * 0.6) + (5ft * 0.6^2) + (5ft * 0.6^3) + ...
I hope this explanation helps you understand how to write the infinite geometric series representing the distance traveled by the table tennis ball.