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?

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) π (v2/g) (B) π (v4/g2) (C) π 2(v4/g2) (D) π 2(v2/g2)

Tardigrade Admin · Accepted Answer

The area in which bullet will spread =π r2 For maximum range, R textmax=(v2/g) [when θ =45° ] ∴ Maximum area =π R textmax2=π ((v2/g))2=(π v4/g2)

Q. 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?

$π \frac{v ^{2}}{g}$

$π \frac{v ^{4}}{g ^{2}}$

$π^{2} \frac{v ^{4}}{g ^{2}}$

$π^{2} \frac{v ^{2}}{g ^{2}}$

The area in which bullet will spread $= π r^{2}$
For maximum range, $R_{max} = \frac{v ^{2}}{g}$ [when $θ = 4 5^{\circ}$ ]
$∴$ Maximum area $= π R_{max}^{2} = π (\frac{v ^{2}}{g})^{2} = \frac{π v ^{4}}{g ^{2}}$

Q. 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?

πgv2​

πg2v4​

π2g2v4​

π2g2v2​