A bullet fired into a fixed target loses half of its velocity in penetrating 20cm. How much further (in cm) it will penetrate before coming to rest?

Initial velocity  $u=u$
Final velocity  $V=\frac{u}{2}$
Distance   $S_1=20cm$
From equation of motion moving with uniform acceleration $V^2-u^2=2aS$ 
${\left(\frac{u}{2}\right)}^2-u^2=2a\left(20\right)$ 
$\Rightarrow -\frac{3u^2}{4}=40a\mathrm{........}\left(1\right)$ 
Step-II
Initial velocity $u_2$ =Final velocity in the previous case$=\frac{u}{2}$
Final velocity  $V_2=0$
Distance travelled  $S_2=x$
From equation  $V_2^2-u_2^2=2a{S}_2$
$\Rightarrow 0^2-{\left(\frac{u}{2}\right)}^2=2ax$ 
$\Rightarrow -\frac{u^2}{4}=2ax\mathrm{..........}\left(2\right)$ 
From (1) and (2) 
$\begin{array}{l}3=\frac{20}{x}\\ \therefore x=\frac{20}{3}=6.67\mathrm{cm}\end{array}$