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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 $u/3$. 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
Explanation
Using third equation of motion between I and $II v^{2} - u^{2} = 2$ as $\Rightarrow (u/3)^{2} = u^{2} - 2a \times 24$ $\Rightarrow 2a(24) = 8u^{2}/9$ Using third equation of motion again between II and III $0 = (u/3)^{2} - 2as \Rightarrow u^{2}/9 = 2as$ From equation (i) and (ii) $2a24 = 8(2as)$ $\Rightarrow s = 3 cm$ Length of wooden block = $24 + 3 = 27 cm$