Question

A bullet fired into a fixed target looses half of its velocity in penetrating $15cm$. Before coming to rest, it can penetrate a further distance of:

• A. $5cm$
• B. $15cm$
• C. $7.5cm$
• D. $10cm$

Answer 1

The correct option is A $5cm$

Assuming that the bullet has only Kinetic Energy ($KE$ ) initially.

Let initial velocity be $v$.

So, final velocity is $v/2$.

Energy lost is $\frac{1}{2}m{v}^2-\frac{1}{2}m(v/2{)}^2=\frac{1}{2}m(\frac{3}{4}{v}^2)$

$=\frac{3}{4}\left(\frac{1}{2}m{v}^2\right)$

Remaining energy $=\frac{1}{4}\left(1/2m{v}^2\right).$

Since, $\frac{3}{4}KE$ is lost in $15cm$ penetration,

Hence $\frac{1}{4}KE$ would penetrate to $\frac{15}{3}=5cm$

So, the distance further travelled by the bullet before coming to rest $=5cm.$