Question

In the CID serial which comes on TV, Abhijeet fires a bullet of mass 100g with a speed of 100 m/s on a soft plywood of thickness 4 cm. The bullet emerges with 10 % of its initial kinetic energy. Find the emergent speed of the bullet.

Answer 1

Hint:We are given with the mass of the bullet and its initial velocity. Using these two we can find the initial kinetic energy of the bullet. The thickness of the block is 4 cm and the bullet comes out and has 10 % of its initial kinetic energy, so we can calculate the emergent speed using this.

Complete step by step answer:
Given mass, m= 100 g = 0.1 kg
Initial speed, u= 100 m/s
Initial kinetic energy, \[{{K}_{i}}=\dfrac{m{{u}^{2}}}{2}=\dfrac{0.1\times {{100}^{2}}}{2}=500J\]
Given that it emerges with 10 % of its initial kinetic energy, so final kinetic energy is
\[\begin{align}
&{{K}_{f}}=10\%{{K}_{1}} \\
&\Rightarrow{{K}_{f}} =0.1\times 500 \\
&\Rightarrow{{K}_{f}} =50J \\
\end{align}\]
But final kinetic energy can be given as
\[\begin{align}
&{{K}_{f}}=\dfrac{m{{v}^{2}}}{2} \\
&\Rightarrow 50=\dfrac{0.1\times {{v}^{2}}}{2} \\
&\Rightarrow 100=0.1{{v}^{2}} \\
&\Rightarrow {{v}^{2}}=1000 \\
&\therefore v=31.62m/s \\
\end{align}\]

So, the bullet comes out with a speed of 31.62 m/s.

Additional Information:
Energy is a scalar quantity, i.e., it does not depend on direction, and it is always positive. Kinetic energy being negative does not make any sense because we are having a square of velocity and for sure mass can never be negative.

Note:In this question we were given the thickness of the Planck in which the bullet was fired but it was misleading as we do not have to make use of it. The question language makes it confusing that we have to use conservation of momentum, but the above-mentioned way is the most simple and lucid.