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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28 cm

27 cm

24 cm

30 cm

answer is B.

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Detailed Solution

Assuming the acceleration is constant using equation of motion

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

If the velocity is changing from (u/3) to zero over a distance of s’

$\begin{aligned} (0)^{2} - {(\frac{u}{3})}^{2} = 2 a s^{'} \\ \frac{- u^{2}}{9} = 2 (\frac{- u^{2}}{54}) s^{'} = s^{'} = 3 cm \end{aligned}$

So, the total distance penetrated = 24 + s’= 24+3 = 27 cm

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