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

Let the thickness of one plank is s 

if bullet enters with velocity u then it leaves with velocity 

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

from ${\mathrm{v}}^2={\mathrm{u}}^2-2\mathrm{as}$

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

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

$0={\mathrm{u}}^2-2\mathrm{ans}$

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

$\Rightarrow \mathrm{n}=10.25$

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