Question

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

• A. $2\sqrt{10}m{s}^{-1}$
• B. $20\sqrt{10}m{s}^{-1}$
• C. $10\sqrt{2}m{s}^{-1}$
• D. $10\sqrt{20}m{s}^{-1}$

Answer 1

Answer: (B)

$m=50g,u=200m/s,t=2cm$
InitialKE $=\frac{1}{2}m{u}^2=\frac{1}{2}\times \frac{50}{1000}\times 400\times 10^2=1000kg-m/s^2$
Final KE $=\frac{1}{10}($ InitialKE $)=\frac{1}{10}\times 1000=100kg-m/s^2$
$\therefore \frac{1}{2}m{v}^2=100⟶\frac{1}{2}\times \frac{50}{1000}{v}^2=100$
$v^2=40\times 100⟶v=20\sqrt{10}m/s$