Question

A bullet moving with a velocity of $30\sqrt{2}m/s$ is fired into a fixed target. It penetrated into the target to the extent of $S$ meters. If the same bullet is fired into a target of thickness $\frac{S}{2}$ meters and of the same material with the same velocity, the bullet comes out of the target with velocity:

• A. $20m/s$
• B. $30m/s$
• C. $20\sqrt{2}m/s$
• D. $10\sqrt{2}m/s$

Answer 1

Answer: (B)

$30m/s$

Let the mass of the bullet be $m$ and the force exerted by the target on the bullet be $F$

Given : $u=30\sqrt{2}$ $m/s$

Using work-energy theorem : $W=\Delta K.E=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$

Case (1) : Penetrating distance $=S$ and $v=0$

$\therefore$ $-FS=0-\frac{1}{2}m(30\sqrt{2}{)}^2$ ..........(1)

Case (2) : Penetrating distance $=\frac{S}{2}$ and final velocity of bullet be $v^{\prime }$

$\therefore$ $-F\frac{S}{2}=\frac{1}{2}m(v^{\prime }{)}^2-\frac{1}{2}m(30\sqrt{2}{)}^2$ ..........(2)

Dividing (1) and (2), $2=\frac{-(30\sqrt{2}{)}^2}{(v^{\prime }{)}^2-(30\sqrt{2}{)}^2}$

or, $(v^{\prime }{)}^2=1800-900$ $⟹(v^{\prime }{)}^2=900$

$⟹$ $v^{\prime }=30$ $m/s$