(B) Let the retardation produced by the wooden block be $a$. Using the equation of motion $v^2 = u^2 + 2as$:For the first $24\,cm$ $(s_1 = 24\,cm)$:$(

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(B) Let the retardation produced by the wooden block be $a$. Using the equation of motion $v^2 = u^2 + 2as$:For the first $24\,cm$ $(s_1 = 24\,cm)$:$(\frac{u}{3})^2 = u^2 - 2a(24)$$\frac{u^2}{9} = u^2 - 48a$$48a = u^2 - \frac{u^2}{9} = \frac{8u^2}{9}$$a = \frac{8u^2}{9 \times 48} = \frac{u^2}{54}.........(1)$Now,let the total length of the block be $L$. For the entire motion until the bullet comes to rest $(v=0)$:$0^2 = u^2 - 2aL$$2aL = u^2$$L = \frac{u^2}{2a}.........(2)$Substituting the value of $a$ from $(1)$ into $(2)$:$L = \frac{u^2}{2 \times (u^2/54)} = \frac{54}{2} = 27\,cm$.

Class 11 Physics Motion in Straight Line Uniformly Accelerated Motion

Medium

$A$ bullet from a gun is fired into a rectangular wooden block with velocity $u$. When the bullet travels $24\,cm$ through the block along its length horizontally,the velocity of the bullet becomes $\frac{u}{3}$. It then 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 $........\,cm$.

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Motion in Straight Line

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Uniformly Accelerated Motion

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