Question

A man shot a bullet with a speed of 10 m $s^{-1}$ which just penetrates a plank of wood. With what speed should he shoot the bullet so that it passes through 10 similar planks?

• A. 100 m $s^{-1}$
• B. 104 m $s^{-1}$
• C. 10$\sqrt{10}$ m $s^{-1}$
• D. 5$\sqrt{10}$ m $s^{-1}$

Answer 1

The correct option is C 10$\sqrt{10}$ m $s^{-1}$

Energy of a single bullet$=\frac{1}{2}m{v}^2=\frac{1}{2}m\times 100=50m$

Energy should be 10 times of this to pass through 10 planks$=10\times 50m=500m$

And this equal to new energy of the bullet,mass remaining same:

$500m=\frac{1}{2}m{v}^{\prime 2}$

$v^{\prime 2}=1000$

$v^{\prime }=\sqrt{1000}=10\sqrt{10}m/s$