A bullet from a gun fired on a rectangular wooden block with velocity . When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes . Then it further penetrates into the block in the same direction before coming t

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Solution

Q.
A bullet from a gun 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 [2023]

1 28 cm

2 30 cm

3 27 cm

4 24 cm

Ans.
(3)

When bullet covers 0.24 m, speed is $\frac{u}{3}$

Here constant retardation $(a)$ will be provided to the bullet by frictional force.

Now, applying equation of kinematics,

$\frac{u^{2}}{9} = u^{2} - 2 a (0.24) \Rightarrow \frac{8}{9} u^{2} = a (0.48)$

or $a = \frac{8 u^{2}}{9 \times 0.48}$ ...(i)

Now, for further motion, let $x$ be the distance when bullet stops.

$0 = \frac{u^{2}}{9} - 2 a x,$

$\Rightarrow 2 a x = \frac{u^{2}}{9} \Rightarrow a = \frac{u^{2}}{18 x}$ ...(ii)

From equation (i) and (ii), we get

$\frac{8 u^{2}}{9 \times 0.48} = \frac{u^{2}}{18 x} \Rightarrow x = \frac{9 \times 0.48}{8 \times 18} = 3 cm$

Thus, total length = $24 cm + 3 cm = 27 cm$

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