Question

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

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

Answer 1

Answer: (D)

According to work-energy theorem,
$W = \Delta K$
Case I : $-F\times3=\,\frac{1}{2} m\left(\frac{v_{0}}{2}\right)^{2}-\frac{1}{2}\, mv^{2}_{0}$
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.
$\therefore -F \left(3+ s\right) = K_{f}-k_{i} =\frac{1}{2}\,mv^{2}_{0}$
or $\frac{1}{4} \left(3+s\right)=1$
or $\frac{3}{4}+\frac{s}{4}=1$
$\therefore s = 1\, cm$