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

Answer 1

The correct option is B 1.0 cm

Let initial velocity of the bullet = u
After penetrating 3 cm ite velocity becomes $\frac{u}{2}$
From $v^2=u^2-2as$

${\left(\frac{u}{2}\right)}^2=u^2-2a\left(3\right)$

$\Rightarrow 6a=\frac{3u^2}{4}\Rightarrow a=\frac{u^2}{8}$
Let further it will penetrate through distance x and stops at point C.
For distance BC, $v=0,u=‘\frac{u}{2},s=x,a=\frac{u^2}{8}$

From $v^2=u^2-2as\Rightarrow 0={\left(\frac{u}{2}\right)}^2-2\left(\frac{u^2}{8}\right).x$
$\Rightarrow x=1cm.$