A bullet travelling with a speed of 150 mis is just
able to pierce a plank 4 cm thick. What should be
the velocity of the bullet so that it is just able to
pierce a plank of thickness 16 cm?
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v=300m/sec
It is given that the bullet travels 4 cm at a velocity of 150 m/s.
First of all, we calculate the Energy of the bullet as follows:
\begin{gathered}E=\frac{1}{2}mv^2\\ \\E=\frac{1}{2}m(150)^2\\ \\E=11250m\end{gathered}
E=
2
1
mv
2
E=
2
1
m(150)
2
E=11250m
.
We need to calculate the speed if the bullet will travel 16 cm. Therefore, it will have an energy of 16/4 of the original energy.
\begin{gathered}E=\frac{16}{4}*11250m=45*10^3m\\ \\45*10^3m=\frac{1}{2}mv^2\\ \\ v^2=90*10^3\\v=300\:m/sec\end{gathered}
E=
4
16
∗11250m=45∗10
3
m
45∗10
3
m=
2
1
mv
2
v
2
=90∗10
3
v=300m/sec
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