Question

A police man fires a bullet of mass $25grams$ with speed of $100m/s$ in wooden piece of thickness $2.0cm$. The bullet leaves the wooden piece with only $10\%$ of its initial kinetic energy. By how much percentage has the speed of bullet been reduced?

Answer 1

Given,

Mass of the bullet is $m_b=25gm=0.025Kg$

Initial velocity of bullet $u_b=100m/s$

From the conservation of energy

Initial kinetic energy = $\frac{1}{2}{m}_b{u}_b^2=\frac{10}{100}\left(\frac{1}{2}{m}_b{u}_b^2\right)+\frac{1}{2}{m}_b{v}_b^2$

10 % (Initial kinetic energy) = final kinetic energy

$\frac{10}{100}\left(\frac{1}{2}{m}_b{u}_b^2\right)=\frac{1}{2}{m}_b{v}_b^2$

$v_b=\sqrt{0.1u_b^2}=\sqrt{0.1\times 100}=\sqrt{10}m{s}^{-1}$

Hence, final velocity is $\sqrt{10}m{s}^{-1}$