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. 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 its 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,

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.