Question

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

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

Answer 1

Answer: (B)

$20\sqrt{10}\,ms^{-1}$

Answer 2

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