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A bullet from a gun is fired on a rectangular wooden block with velocity uu. When bullet travels 2424 cm through the block along its length horizontally, velocity of bullet becomes u3\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

A

27 cm

B

24 cm

C

28 cm

D

30 cm

Step-by-Step Solution

Using v2=u2+2asv^2 = u^2 + 2as, for the first part: (u3)2=u2+2a(24)  ⟹  −8u29=48a  ⟹  a=−u254(\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 xx: 02=(u3)2+2ax  ⟹  0=u29+2(−u254)x  ⟹  u29=u227x  ⟹  x=30^2 = (\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=2724 + 3 = 27 cm.

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