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We have an increasing number of books on a bookshelf. Every year, 2 books are added and each book is twice as long as the previous book. At the beginning of 1935 the volume was 1 cm thick. We define the 'velocity of the front cover' as the thickness of that volume divided by the number of seconds in six months.Determine the year when the front cover of the volume stacked will exceed the velocity of light. I tried to do it like this:

$$ v = \dfrac{ \text {thickness volume}}{ \text {number of seconds in 6 months}}$$

$$ \text{thickness volume} = 3 \times 10^8 \cdot 15552000 = 4.6656 \times 10^{15}$$

$$ \log_{10}(ans) \approx 15.7$$

So that's the thickness of the book which exceeds the velocity of light. Since the volumes become four times as big every year, if we calculate in logs, every year the books become $\log_{10}(4)$ bigger. So I get $$\dfrac{15.66..}{\log_{10}{4}} \approx 26.02 $$

So my answer would be that in the year $26+1935 = 1961$ the velocity would exceed that of light. Which is a wrong answer, but why?

Phaptitude
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    What units are your numbers in? –  Oct 07 '13 at 10:56
  • @RahulNarain Thanks, you should post that hint as an answer – Phaptitude Oct 07 '13 at 11:03
  • Depending on the printing and stacking syle, the velocity could be affected by a factor of $2$. E.g. books could printed with the front cover on the right when looking at the spine (European) or on the left (Japanese, Hebrew etc), and stacking on the bookshelf could be from left to right or right to left. – Henry Oct 07 '13 at 11:06

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Your measurement of the speed of light is in meters per second, but your books are moving in speeds of centimeters per second.

abiessu
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