Question

A bullet fired into a fixed target loses half of its velocity after penetrating $3cm$. How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion ?

• A. $3.0cm$
• B. $2.0cm$
• C. $1.5cm$
• D. $1.0cm$

Answer 1

Answer: (D)

According to work-energy theorem,
$W=\Delta K$
Case I : $-F\times 3=\frac{1}{2}m{\left(\frac{v_0}{2}\right)}^2-\frac{1}{2}m{v}_0^2$
where, $F$ is resistive force and $v_0$ is initial speed.
Case II : Let, the further distance travelled by the bullet before coming to rest is s.
$\therefore -F\left(3+s\right)=K_f-k_i=\frac{1}{2}m{v}_0^2$
or $\frac{1}{4}\left(3+s\right)=1$
or $\frac{3}{4}+\frac{s}{4}=1$
$\therefore s=1cm$