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
Explanation:
Distance covered by ball when it touches ground for the first time = 350 m.
Distance travelled when it touches for the second time = 2 × (4/5) × 350 m
Distance travelled when it touches for the third time = 2 × (4/5) × (4/5) × 350 m
∴ Total distance = 350 + [2 × (4/5) × 350] + [2 × (4/5) × (4/5) × 350] + …= 350 + [2 × (4/5) × 350][(1 + (4/5) + (4/5)2 + …]
The last term above is an infinite G.P. with a = 1 and r = 4/5
The sum of such an infinite G.P. = a/(1 – r) = 1/([1 – (4/5)] = 1/(1/5) = 5
∴ Total distance = 350 + [2 × (4/5) × 350](5) = 350 + 8(350) = 9(350) = 3150 m
Hence, option (c).
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