Question

A bullet fired into a wooden block loses half of its velocity after penetrating $40\text{cm}.$ It comes to rest after penetrating a further distance of

• A. $\frac{22}{3}\text{cm}$
• B. $\frac{40}{3}\text{cm}$
• C. $\frac{20}{3}\text{cm}$
• D. $\frac{22}{5}\text{cm}$

Answer 1

The correct option is B $\frac{40}{3}\text{cm}$

Since, the bullet loses half of its velocity after penetrating $40\text{cm}$
Let say, initial velocity of the bullet is $u$
then, after losing half of velocity, final velocity at this moment will be $v=\frac{u}{2}$
From equation of motion we have
$v^2-u^2=2as\Rightarrow {\left(\frac{u}{2}\right)}^2-u^2=2as$
or, $\Rightarrow a=-\frac{3u^2}{8s}$
For, later part of the penetration, final velocity will be zero i.e. $v=0$
$\Rightarrow 0^2-{\left(\frac{u}{2}\right)}^2=2a{s}^{{}^{\prime }}$
$\Rightarrow s^{{}^{\prime }}=-\frac{u^2}{8}(-\frac{8s}{3u^2})=\frac{s}{3}$
$\Rightarrow s^{{}^{\prime }}=\frac{40}{3}\text{cm}$