IIFT 2016 Question Paper Question 105

Question 105

A child, playing at the balcony of his multi-storied apartment, drops a ball from a height of 350 m. Each time the ball rebounds, it rises 4/5th of the height it has fallen through. The total distance travelled by the ball before it comes to rest is


Total distance covered by the ball will be = $$350+2(\frac{4}{5}*350+(\frac{4}{5})^{2}*350+(\frac{4}{5})^{3}*350+...)$$

                                                           = $$350+2*350(\frac{4}{5}+(\frac{4}{5})^{2}+(\frac{4}{5})^{3}+...)$$

                                                           = $$350+2*350(\frac{\frac{4}{5}}{1-\frac{4}{5}})$$

                                                           = $$350+2*350*4$$ =$$3150$$

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