Question

# A ball falls from a height of 100 mts. on a floor. If in each rebound, it describe (4/5)th height of the previous falling height, then the total distance travelled by the ball before it come to rest is

Solution

## The total height it travel before it comes to rest is $$S=100+2(100)\dfrac{4}{5}+2(100)\left(\dfrac{4}{5}\right)+.....................\infty$$$$S=100+2(100)\dfrac{4}{5}\left(1+\dfrac{4}{5}+\dfrac{4^2}{5^2}+.............+\infty \right)$$$$S=100+160(\dfrac{1}{\tfrac{1}{5}})=900m$$Mathematics

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