Question

A bullet when fired at a target with a velocity of $100m/s$ penetrates one metre into it. If the bullet is fired at a similar target with a thickness $0.5m$ . Then, it will emerge from it with a velocity of

• A. $50\sqrt{2}m/s$
• B. $\frac{50}{\sqrt{2}}m/s$
• C. $50m/s$
• D. $10m/s$

Answer 1

Answer: (A)

Let $v$ be the velocity with which the bullet will energy. Now,
Change in kinetic energy $=$ Work done.
In first case,
$\frac{1}{2}m(100{)}^2=\frac{1}{2}m(0{)}^2=F\times 1...(i)$
In second case,
$\frac{1}{2}m(100{)}^2-\frac{1}{2}m{v}^2=F\times 0.5...(ii)$
Dividing Eq. (ii) by Eq. (i), we get
$\frac{\left(100^2\right)-v^2}{(100{)}^2}=\frac{0.5}{1}=\frac{1}{2}$
$1-\frac{v^2}{(100{)}^2}=\frac{1}{2}$
${\left(\frac{v}{100}\right)}^2=\frac{1}{2}$
$v=\frac{100}{\sqrt{2}}=50\sqrt{2}m/s$