Question

In CID serial (on TV), Abhijeet fires a bullet of mass $100$$g$ with a speed of $100$$m{s^{ - 1}}$ on a soft plywood of thickness $4$$cm$. The bullet emerges with $10\% $ of its initial KE. Find the emergent speed of the bullet.

Answer 1

Hint: When CID officer Abhijeet fires the bullet with certain speed, it hits the soft plywood. Due to the resistance that will be offered by the plywood, the bullet will slow down. As a result. The kinetic energy of the bullet will decrease and the final kinetic energy will be less than the initial kinetic energy. Value of this kinetic energy is already given to you. By applying basic mathematics, you can find the final speed or the emergent speed of the bullet.

Complete step by step answer:
Let the initial speed with which the bullet is fired be $u$. After the impact, let the emergent speed of the bullet be $v$. So, the initial kinetic energy of the bullet will be ${K_i} = \dfrac{1}{2}m{u^2}$ and the final kinetic energy after the impact is given as ${K_f} = \dfrac{1}{2}m{v^2}$.You are given that the final kinetic energy after impact is $10\% $ of the initial kinetic energy before impact. Mathematically,
$
{K_f} = 10\% {K_i} \\
\Rightarrow{K_f} = \dfrac{{{K_i}}}{{10}} \\
$
Let us substitute the value of initial and final kinetic energy in the above equation, we get,
$
\dfrac{1}{2}m{v^2} = \left( {\dfrac{1}{{10}}} \right)\dfrac{1}{2}m{u^2} \\
\Rightarrow{v^2} = \dfrac{{{u^2}}}{{10}} \\
\Rightarrow v = \dfrac{u}{{\sqrt {10} }} \\ $
The emergent speed of the bullet is given as $v = \dfrac{u}{{\sqrt {10} }}$. In the question above, it is given that the initial velocity $u = 100$$m{s^{ - 1}}$. Let us substitute this value in the above expression, we get,
$v = \dfrac{u}{{\sqrt {10} }} \\
\Rightarrow v = \dfrac{{100}}{{\sqrt {10} }} \\
\therefore v = 10\sqrt {10}\,m{s^{ - 1}}$

Hence, the emergent speed of the bullet is $10\sqrt {10}\,m{s^{ - 1}}$.

Note: Remember that kinetic energy of an object is given as the product of mass and the square of velocity divided by two. Remember the method we used to find the final velocity of the bullet after the impact. Here, extra data about the mass of the bullet and the thickness of the plywood was given, which was not required.