Question

A large number of bullets are fired in all direction with same speed, what is the maximum area of their spread ?

• A. $\frac{\pi v^2}{g}$
• B. $\frac{{\pi }^2{v}^4}{g^2}$
• C. $\frac{\pi v^4}{g^2}$
• D. $\frac{{\pi }^2{v}^2}{g^2}$

Answer 1

The correct option is C $\frac{\pi v^4}{g^2}$

$\text{The range of bullets fired is given by}\Rightarrow$

$R=\frac{u^2}{g}\left(\sin 2\theta \right)$

$\text{for maximum range,}\theta ={45}^{\circ }\text{so that}\left(\sin 2\theta \right)=1$

$\text{and}R=\frac{u^2}{g}$

$\text{Bullets are fired in all directions with}$

$\text{v' velocity, so the area covered will be}$

$\text{a horizontal circle.}$

$\text{So radius of circle}=\mathrm{Range}\left(R\right)=\frac{u^2}{g}$

$\text{Area of Circle}=\pi R^2[R>r\text{adius}]$

$\text{So,}\pi R^2=\pi {\left(\frac{u^2}{g}\right)}^2=\pi \frac{u^4}{g^2}$

$\text{Since, veloity of bullets fired is denoted}$

$\text{by}v\text{here, so maximum area covered}$

$\text{will be}\left(\frac{\pi v^4}{g^2}\right)$

$\text{option (c) is the correct answer.}$