Question

A bullet fired into a fixed target loses half of its velocity after penetrating $4cm$. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

• A. $0.2cm$
• B. $5cm$
• C. $2cm$
• D. $1.33cm$

Answer 1

Answer: (D)

Let the initial velocity of the bullet $=u$
After penetrating its final velocity $=\frac{u}{2}$
From $v^2-u^2=2$ as
${\left(\frac{u}{2}\right)}^2-u^2=2\times a\times 4$
$\frac{u^2}{4}-u^2=2\times a\times 4$
$\frac{-3u^2}{4}=8\times a\Rightarrow a=\frac{-3u^2}{32}$
Bullet will further penetrate after penetrate $4cm$.
Initial velocity $=\frac{u}{2}$
Final velocity $=0$
From $v^2-u^2=2$ as
$0^2-{\left(\frac{u}{2}\right)}^2=2\times \frac{-3u^2}{32}\times s$
$\frac{-u^2}{4}=\frac{-3u^2}{16}\times s$
$\Rightarrow s=\frac{4}{3}=1.33cm$