Question

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?​

Answer 1

Explanation:

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Answer 2

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