Question

A bullet when fired into a target loses half of its velocity after penetrating $20\, cm$. Further distance of penetration before it comes to rest is

• A. 6.66 cm
• B. 3.33 cm
• C. 12.5 cm
• D. 10 cm

Answer 1

The Correct Option is A

Given, Initial velocity, $U=v$
Final velocity, $V=\frac{V}{2}$
Distance, $s=20 \,cm$
Let, the further distance of penetration before it comes to rest be $x$.
$V^{2} =U^{2}-2 a s $
$\left(\frac{V}{2}\right)^{2} =v^{2}-2 a \times 20 $
$40\, a =v^{2}-\frac{v^{2}}{4} $
$40\, a =\frac{3 v^{2}}{4}\,...(i) $
and $v^{2}=u^{2}+2 a s$
$v^{2}=0+2 a \times(20+x)$
$v^{2}=2 \times \frac{3}{160} v^{2} \times(20+x)$ [From E(i)]
$ 1 =\frac{3}{80}(20+x) $
$\frac{80}{3} =20+x$
$ x =\frac{80}{3}-20 $
$x =\frac{80-60}{3} $
$x =\frac{20}{3}=6.66\, cm $