A bullet fired from a gun into a rectangular wooden block with velocity $u$. When the bullet travels

Question

A bullet fired from a gun into a rectangular wooden block with velocity $u$. When the bullet travels 30 cm through the block horizontally, the velocity of the bullet becomes $u/2$. It then further penetrates into the block in the same direction before coming to rest exactly at the other end. The total length of the block is

Professor PC Thomas Classes · Answer

Let acceleration be $a$. Using $v^2 - u^2 = 2as$, $(u/2)^2 - u^2 = 2a(0.3) \implies \frac{u^2}{4} - u^2 = 0.6a \implies -\frac{3u^2}{4} = 0.6a \implies a = -\frac{5u^2}{4}$. Let the further penetration distance be $x$. $0^2 - (u/2)^2 = 2ax \implies -\frac{u^2}{4} = 2(-\frac{5u^2}{4})x \implies \frac{1}{4} = \frac{10x}{4} \implies x = 0.1 \mathrm{~m} = 10 \mathrm{~cm}$. Total length = $30 + 10 = 40 \mathrm{~cm}$.