If a ball is dropped from 40m and every bounce after, the distance bounced is 1/2 that of the bounce before.

a)How long till the ball stops bouncing (# of bounces)?

b) What is the total distance the ball has fallen once it comes to rest?

use 40,20,10,5,2.5,1.25... as the Series.

Question

If a ball is dropped from 40m and every bounce after, the distance bounced is 1/2 that of the bounce before.

a)How long till the ball stops bouncing (# of bounces)?

b) What is the total distance the ball has fallen once it comes to rest?

use 40,20,10,5,2.5,1.25... as the Series.

anonymous · Answer

This is the formula:
$$\sum_{k=1}^{\infty} 40(\frac{ 1 }{ 2 })^{k-1}$$

loser66 · Answer

Theoretically, it will never get stop. Actually, it stops due to gravity force and friction force. In this case, I don't know how to answer. 
The series 40,20,10, 5,....... converge to 0 and by taking limit of the term $a_n = (1/2) a_{n-1}$ but that is the LIMIT, not the number.