Question

A rifle bullet loses $1/{20}^{th}$ of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is

• A. $5$
• B. $10$
• C. $11$
• D. $20$

Answer 1

The correct option is C $11$

Let the thickness of one plank is s

if bullet enters with velocity u then it leaves with velocity

$v=(u-\frac{u}{20})=\frac{19}{20}u$

from $v^2=u^2-2as$

$\Rightarrow {\left(\frac{19}{20}u\right)}^2=u^2-2as\Rightarrow \frac{400}{39}=\frac{u^2}{2as}$

Now if the n planks are arranged just to stop the bullet then again from $v^2=u^2-2as$

$0=u^2-2ans$

$\Rightarrow n=\frac{u^2}{2as}=\frac{400}{39}$

$\Rightarrow n=10.25$

As the planks are more than 10 so we can consider $n=11$