Wrecking Ball

Calculus Level 1

The ball rolled for a distance of 32 cm in the first second, 16 cm after the second seconds, 8 cm in the third seconds and so on. What is the distance that the ball traveled before it stops?


The answer is 64.

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3 solutions

Using the Infinite Geometric Series, a 1 a_{1} = 32 and the common ratio is 1 2 \frac{1}{2}

Simplifying, we have S n S_{n} = a 1 1 r \frac{a_{1}}{1- r} = 32 1 1 2 \frac{32}{1- \frac{1}{2}} = 64

Hence the answer is 64 \boxed{64}

Nice solution :)

Brian Dela Torre - 5 years, 4 months ago

32 , 16 , 8 , . . . 32,16,8,... \implies Observed that it is a geometric progression with a common ratio of 8 16 = 16 32 = 0.5 \dfrac{8}{16}=\dfrac{16}{32}=0.5

In here we are finding the sum of the geometric progression with infinitely many terms. If S S represents this sum then

S = a 1 1 r S=\dfrac{a_1}{1-r} where a 1 a_1 is the first term and r r is the common ratio. Substituting, we have

S = 32 1 0.5 = 64 S=\dfrac{32}{1-0.5}=\boxed{64}

Abc Xyz
Mar 1, 2016

Here we see that the terms for distance are decreasing by 2.

They will continue to decrease from 1 2 \frac {1}{2} to 1 4 \frac {1}{4} and so on.

Therefore it is an infinite geometric progression.

So a = 32 and r = 1 2 \frac {1}{2}

Therefore S n = a 1 r = 32 0.5 = 64 S_n = \frac {a}{1-r} = \frac {32}{0.5} = 64

So the answer is 64 \boxed {64}

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