Question

A bullet loses $1/20$ of its velocity after penetrating a plank. How many planks are required to stop the bullet?

• A. 6
• B. 9
• C. 11
• D. 13

Answer 1

Answer: (B)

The final velocity after it passes the plank is $\frac{19 u}{20}$.

Let $x$ be the thickness of the plank, the deceleration due to resistance of plank, is given by
$v^{2}=u^{2}+2 a s$
where $v$ is final velocity, $u$ is initial velocity, $a$ is acceleration and $s$ is displacement.
Here $v=\frac{19}{20} u$
$\therefore \left(\frac{19}{20} u\right)^{2}=u^{2}+2 a x$
$\Rightarrow 2 a x=\frac{-39}{400} u^{2}$
Suppose the bullet is stopped after passing through $n$ such planks. Then the distance covered by bullet is $n x$.
$\therefore 0=\left(\frac{19}{20}\right)^{2} u^{2}+2 an x$
$\Rightarrow -\left(\frac{19}{20}\right)^{2} u^{2}=n \times \frac{-39}{400} u^{2} $
$\Rightarrow n=\frac{361}{39} \approx 9$