Question

A bullet is fired through a gun. It passes through a wooden plank which reduces its velocity by ${\frac{1}{20}}^{th}$ of the initial velocity. How many are such planks required to stop it completely?

Answer 1

Let the thickness of one plank be $d$ and the acceleration provided by the plank be $a$.
As per the question, ${\left(\frac{19v_0}{20}\right)}^2=v_0^2-2ad\Rightarrow \frac{361}{400}\times v_0^2=v_0^2-2ad\Rightarrow a=\frac{39}{400}\frac{v_o^2}{2d}$
Now, let on passing through $n$ plancks, the final velocity of bullet become zero.
So, $0=v_0^2-2nad\Rightarrow n=\frac{v_o^2}{2ad}=\frac{400}{39}$
The minimum number of planks needed = smallest integer greater than$\frac{400}{39}=11$.