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 u3. 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.

Assuming the acceleration is constant using equation of motion (u3)2−u2=2a(24) ⇒−8u29=2(a)(24) ⇒a=−u254If the velocity is changing from (u/3) to zero over a distance of s’ (0)2−(u3)2=2as′ −u29=2(−u254)s′=s′=3cmSo, the total distance penetrated = 24 + s’= 24+3 = 27 cm

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 u3. 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.

Assuming the acceleration is constant using equation of motion (u3)2−u2=2a(24) ⇒−8u29=2(a)(24) ⇒a=−u254If the velocity is changing from (u/3) to zero over a distance of s’ (0)2−(u3)2=2as′ −u29=2(−u254)s′=s′=3cmSo, the total distance penetrated = 24 + s’= 24+3 = 27 cm

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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 $\frac{u}{3}$ . 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.

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30 cm

27 cm

24 cm

28 cm

answer is B.

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Detailed Solution

Assuming the acceleration is constant using equation of motion

$\begin{aligned} {(\frac{u}{3})}^{2} - u^{2} = 2 a (24) \\ \Rightarrow \frac{- 8 u^{2}}{9} = 2 (a) (24) \\ \Rightarrow a = \frac{- u^{2}}{54} \end{aligned}$