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.

Solution

## Each five ball attains half ofprevious heightso total distance travelled byball before it comes to restwill be$$D=4+2+1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+---$$It is a G.P with common ratio $$\dfrac{1}{2}$$& G.P continues till infinity.so sum of infinite $$G.P=\dfrac{a}{1-r}$$$$=\dfrac{4}{1-\dfrac{1}{2}}=\dfrac{4}{\dfrac{1}{2}}=8m$$Mathematics

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