Question

When a bullet is fired at a target, its velocity decreases by half after penetrating $30cm$into it. The additional thickness it will penetrate before coming to rest is

• A. $30cm$
• B. $40cm$
• C. $10cm$
• D. $50cm$

Answer 1

The correct option is C

$10cm$

Step 1. Given data:

Initial velocity = $v$ $m{s}^{-2}$

Final velocity after penetration = $\frac{v}{2}$ $m{s}^{-2}$

Displacement $\left(s\right)$ = $30cm$

Step 2. Formula used:

Taking the equation of motion into account, $v^2=u^2+2as$, where$v$ is the final velocity, $u$is the initial velocity, $a$ is the acceleration and $s$ is the displacement.

Step 3. Calculation:

Therefore, $v^2=u^2+2as$

Here,

${(v/2)}^2=v^2+2a\times 30$

$-60a=v^2-v^2/4$

$-60a=3v^2/4$

$a=\frac{-v^2}{80}cm{s}^{-2}$

Allow the bullet to penetrate $xcm$ before coming to a stop, as a result

$v{\text{'}}^2=u{\text{'}}^2+2as\text{'}$

$\Rightarrow 0={(v/2)}^2+2(-v^2/80)x$

$$\begin{gathered} \Rightarrow v^2/4=\left(v^2/40\right)x \\ \Rightarrow x=\frac{40}{4} \end{gathered}$$

$\Rightarrow x=10cm$

Hence, option (C) is correct.