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 $\frac{19u}{20}$.

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