Question

A large number of bullets are fired in all directions with same speed v. What is the maximum area on the ground on which these bullets will spread

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

Answer 1

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

Area in which bullet will spread $=\pi r^2$
For maximum area, $r=R_{max}=\frac{v^2}{g}[when\theta ={45}^{\circ }]$
Maximum area $\pi R_{max}^2=\pi {\left(\frac{v^2}{g}\right)}^2=\frac{\pi v^4}{g^2}$