Question

In a ballistic demonstration, a police officer fires a bullet of mass $50$ g with speed of $200m{s}^{-1}$ on soft plywood of thickness $2$ cm. The bullet emerges with only $10$ % of its initial kinetic energy. What is the emergent speed of the bullet?

• A. $30$ m/s
• B. $30\sqrt{2}$ m/s
• C. $63.24m/s$
• D. $30\sqrt{10}$ m/s

Answer 1

The correct option is C $63.24m/s$

Mass of bullet $m=50g=0.05kg$

initial velocity of bullet $=u=200m/s$

initial energy of the bullet$,$ $\frac{1}{2}m{u}^2$\frac{1}{2}\left( {0.05} \right)\left( {200\,square} \right) = 1000J$

The bullet emerges with only $10\%$ of its $K.E.$

let the final velocity with which it emerges to be $v$

So$,$ final $K.E$ is $\frac{1}{2}m{v}^2$ $10\%$ of $\frac{1}{2}m{u}^2$

$\frac{1}{2}m{v}^2$ $\left(\frac{10}{100}\right)\times 1000$

$=v^2$ $=100\times \frac{2}{0.05}$

$=v=63.24m/s$

Hence,

option $\left(C\right)$$ is correct answer.