Question

A large number of bullets are fired in all directions with the 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

Answer: (B)

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