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: (a) 24 cm (b) 28 cm (c) 30 cm (d) 27 cm

Answer: (d). First 24 cm: u² - u²/9 = 2a(24) ⇒ 8u²/9 = 48a Remaining part: (u/3)² = 2as ⇒ u²/9 = 2as Divide: 8/1 = 24/s ⇒ s = 3 cm Total length = 24 + 3 = 27 cm. So the answer is (d) 27 cm.

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Inertia, First & Second Laws

A bullet from a gun is fired on a rectangular wooden block with velocity $u$ . When bullet travels $24\text{ cm}$ 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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Answer: (d)

First 24 cm: $u^2 - \frac{u^2}{9} = 2a(24) \Rightarrow \frac{8u^2}{9} = 48a$
Remaining part: $\left(\frac{u}{3}\right)^2 = 2as \Rightarrow \frac{u^2}{9} = 2as$
Divide: $\frac{8}{1} = \frac{24}{s} \Rightarrow s = 3\text{ cm}$
Total length $= 24 + 3 = 27\text{ cm}$ . So the answer is (d) $27\text{ cm}$ .

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