Question

A perfectly ball dropped from a height of $4m$ on a floor rebounds repeatedly and attains each time half of height from where it fell. Find the total distance travelled by the ball before it comes to rest.

Answer 1

Each five ball attains half of

previous height

so total distance travelled by

ball before it comes to rest

will be

$D=4+2+1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+---$

It is a G.P with common ratio $\frac{1}{2}$

& G.P continues till infinity.

so sum of infinite $G.P=\frac{a}{1-r}$

$=\frac{4}{1-\frac{1}{2}}=\frac{4}{\frac{1}{2}}=8m$