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)

9

Answer 2

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 $n x$. $\therefore 0=\left(\frac{19}{20}\right)^{2} u^{2}+2 an x$ $\Rightarrow -\left(\frac{19}{20}\right)^{2} u^{2}=n \times \frac{-39}{400} u^{2}$ $\Rightarrow n=\frac{361}{39} \approx 9$