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
• E. 5 cm

Answer 1

Answer: (A)

6.66 cm

Given, Initial velocity, $U=v$
Final velocity, $V=\frac{v}{2}$
Distance, $s=20cm$

Let, the further distance of penetration before it comes to rest be x.
$V^2=U^2-2as$
${\left(\frac{V}{2}\right)}^2=V^2-2a\times 20$
$40a=V^2-\frac{V^2}{4}$

$40a=\frac{3V^2}{4}$ ...(i)

and $V^2=u^2+2as$
$v^2=0+2a\times (20+x)$
$v^2=2\times \frac{3}{160}{v}^2\times (20+x)$ [From Eq. (i)]
$1=\frac{3}{80}(20+x)$
$\frac{80}{3}=20+x$
$x=\frac{80}{3}-20$
$x=\frac{80-60}{3}$
$x=\frac{20}{3}=6.66cm$