Can anybody help me on this problem please ?
A ball rebounds each time to a height which is half that of the previous
one. If the total distance traveled before coming to rest is 72 meters,
from how high was the ball dropped?
thanks a lot
Can anybody help me on this problem please ?
A ball rebounds each time to a height which is half that of the previous
one. If the total distance traveled before coming to rest is 72 meters,
from how high was the ball dropped?
thanks a lot
The ball falls x m and bounces up 1/2x m and and falls 1/2x m and bounces up 1/4x m....
$\displaystyle \displaystyle x+x+\frac{1}{2}x+\cdots +\frac{1}{2^n}x$
$\displaystyle \displaystyle x+x\left(1+\frac{1}{2}+\cdots +\frac{1}{2^n}\right)$
$\displaystyle \displaystyle x+x\sum_{n=0}^{\infty}\left(\frac{1}{2}\right)^n=x +\frac{a}{1-r}$ Geometric Series.
$\displaystyle \displaystyle a=x, r=\frac{1}{2}$
$\displaystyle \displaystyle x+\frac{x}{1-\frac{1}{2}}=72\Rightarrow x+2x=72\Rightarrow 3x=72\Rightarrow x=24$