Question

In a ballistics demonstration, a police officer fires a bullet of mass $50.0g$ with speed $200m{s}^{-1}$ on soft plywood of thickness $2.00cm$. The bullet emerges with only $10\%$ of its initial kinetic energy. What is the emergent speed of the bullet.

Answer 1

Given:

$m=50$ $g$, $u=200$ $m/s,$ $t=2$ $cm$

$InitialKE=\frac{1}{2}m{u}^2=\frac{1}{2}\times \frac{50}{1000}\times 400\times {10}^2=1000$ $kg-m/s^2$

$FinalKE=\frac{1}{10}\left(InitialKE\right)=\frac{1}{10}\times 1000=100$ $kg-m/s^2$

$\therefore \frac{1}{2}m{v}^2=100⟶\frac{1}{2}\times \frac{50}{1000}{v}^2=100$

$v^2=40\times 100⟶v=20\sqrt{10}$ $m/s$