how high was the ball dropped?

**rcs** · December 18th 2010, 03:54 PM

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

**dwsmith** · December 18th 2010, 04:11 PM

The ball falls x m and bounces up 1/2x m and and falls 1/2x m and bounces up 1/4x m....

$\displaystyle x+x+\frac{1}{2}x+\cdots +\frac{1}{2^n}x$

$\displaystyle x+x\left(1+\frac{1}{2}+\cdots +\frac{1}{2^n}\right)$

$\displaystyle x+x\sum_{n=0}^{\infty}\left(\frac{1}{2}\right)^n=x +\frac{a}{1-r}$ Geometric Series.

$\displaystyle a=x, r=\frac{1}{2}$

$\displaystyle x+\frac{x}{1-\frac{1}{2}}=72\Rightarrow x+2x=72\Rightarrow 3x=72\Rightarrow x=24$

**rcs** · December 19th 2010, 05:13 AM

thanks a lot sir. Long Live. God Bless You

**Archie Meade** · December 19th 2010, 05:50 AM

Originally Posted by rcs

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

Or...

$x+0.5x+0.5x+0.25x+0.25x+0.125x+0.125x+.....=72$

$x(2+0.5+0.25+......)=72\ \Rightarrow\ 2x+x(0.5+0.25+....)=72$

$x(4+1+0.5+0.25+....)=(2)72\ \Rightarrow\ 5x+x(0.5+0.25+....)=(2)72$

$3x=72$

**rcs** · December 19th 2010, 05:53 AM

amazing!

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