A Pingpong Ball dropped from a height of 128 m rebounds on each bounce one-half the distance from which it fell.How far will it travel before coming to rest?

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Infinite geometric Series

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Answer 1 · 2018-08-02T02:29:58

Initial fall $s_1=128m$

Next rise and fall $s_2=2*1/2*128$ m

Next rise and fall $s_3=2*(1/2^2)128$ m

Next rise and fall $s_4=2*(1/2^3)128$ m

So total path traveled is

$S=sum_(I=1}^(i=oo)s_i$

$=128+128(1+1/2+1/2^2+..... "up to" oo)$

$=128+128(1/(1-1/2))$

$=128+128(1/(1/2))=3*128=384$ m