An ideal bouncing ball rebounds each time to a height k (less than 1) times the height it fell from on that bounce. If the initial height is h, find the total distance the ball travels.
Please explain in detail. Thank you so much!
partial sum
2012-09-24 1:10 pm
回答 (1)
2012-09-24 2:28 pm
✔ 最佳答案
Initial height = h1st rebounce and fall again = hk + hk = 2hk
2nd rebounce and fall again = (hk)k + (hk)k = 2hk^2
3rd rebounce and fall again = (hk^2)k + (hk^2)k = 2hk^3 and so on.
So total distance traveled =
h + 2hk + 2hk^2 + 2hk^3 + .......
= h + 2hk(1 + k + k^2 + ......)
= h + 2hk/(1 - k)
= [h(1 - k) + 2hk]/(1 - k)
= h(1 + k)/(1 - k).
收錄日期: 2021-04-29 00:09:25
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120924000051KK00050