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$
In the real world, everything is always in motion. Objects move at a variable or a constant speed. When someone steps on the accelerator or applies brakes on a car, the speed of the car increases or decreases and the direction of the car changes. In physics, these changes in velocity or directional magnitude of a moving object are represented by acceleration.
