A bullet when fired into a target loses half of its velocity after penetrating 40 cm . Further dista

Question

A bullet when fired into a target loses half of its velocity after penetrating 40 cm . Further distance of penetration before it comes to rest is\

Professor PC Thomas Classes · Answer

Let the bullet be fired with velocity v . For first part of penetration,\ Using $3^{	ext {rd }}$ equation of motion, we get $$ \begin{equation*} \left(\frac{\mathrm{v}}{2}ight)^{2}-(\mathrm{v})^{2}=2 \mathrm{a}(40) 	ag{i} \end{equation*} $$ $-\frac{3}{4} v^{2}=80 a$ or $a=-\frac{3 v^{2}}{320}$\ For latter part of penetration,\ Let x be distance travelled by the bullet before it comes to rest. Again, using $3^{	ext {rd }}$ equation of motion, we get\ $0-\left(\frac{\mathrm{v}}{2}ight)^{2}=2 \mathrm{ax}$\ $\mathrm{x}=-\frac{\mathrm{v}^{2}}{8 \mathrm{a}}=-\frac{\mathrm{v}^{2}}{8}\left(\frac{320}{-3 \mathrm{v}^{2}}ight)=13.33 \mathrm{~cm}$ (Using (i))\