Question

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

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

Answer 1

Answer: (B)

$\pi\frac{u^{4}}{g^{2}}$

Answer 2

The maximum area will be equal to area of the circle with radius equal to the maximum range of projectile

Maximum area $\pi r^{2} = \pi\left( R_{\max}()^{2} \right)$ $= \pi\left( \frac{u^{2}}{g} \right)^{2} = \pi\frac{u^{4}}{g^{2}}$

[As $r = {R2}_{\max}$ for θ = 45⁰]