NDA 2021 Maths · Mathematics · Sequences and Series · medium

A ball dropped from a height of 12 m rebounds each time to 2/3 of the height from which it fell. The total distance it travels before coming to rest…

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A ball dropped from a height of

12

m rebounds each time to

\dfrac23

of the height from which it fell. The total distance it travels before coming to rest is

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Answer: (C) $60$ m

Downward distances:

12+8+\tfrac{16}3+\cdots

, infinite GP with

r=\tfrac23

, sum

=\dfrac{12}{1/3}=36

. The upward distances are

36-12=24

. Total

=36+24=60

m; stopping at 36 forgets the upward legs.

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