A bullet from a gun is fired on a rectangular wooden block with velocity $u$. When bullet travels $24$ cm thro

Question

A bullet from a gun is fired on a rectangular wooden block with velocity $u$. When bullet travels $24$ cm through the block along its length horizontally, velocity of bullet becomes $\frac{u}{3}$. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is

Accepted Answer

Using $v^2 = u^2 + 2as$, for the first part: $(\frac{u}{3})^2 = u^2 + 2a(24) \implies -\frac{8u^2}{9} = 48a \implies a = -\frac{u^2}{54}$. For the second part, let the remaining distance be $x$: $0^2 = (\frac{u}{3})^2 + 2ax \implies 0 = \frac{u^2}{9} + 2(-\frac{u^2}{54})x \implies \frac{u^2}{9} = \frac{u^2}{27}x \implies x = 3$ cm. Total length = $24 + 3 = 27$ cm.

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