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

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Solution

The total height it travel before it comes to rest is $S = 100 + 2 (100) \frac{4}{5} + 2 (100) (\frac{4}{5}) + . . . . . . . . . . . . . . . . . . . . . \infty$

$S = 100 + 2 (100) \frac{4}{5} (1 + \frac{4}{5} + \frac{4^{2}}{5^{2}} + . . . . . . . . . . . . . + \infty)$

$S = 100 + 160 (\frac{1}{\frac{1}{5}}) = 900 m$

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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

The total height it travel before it comes to rest is S=100+2(100)45+2(100)(45)+.....................∞S=100+2(100)45(1+45+4252+.............+∞)S=100+160(115)=900m