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3-2.Motion in Plane
medium
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${\pi ^2}\frac{{{v^2}}}{{{g^2}}}$
Solution
(b) Area in which bullet will spread = $\pi {r^2}$
For maximum area, $r = {R_{\max }} = \frac{{{v^2}}}{g} [{\rm{when }} \theta \,\, = 45^\circ ]$
Maximum area $\pi \;R_{\max }^2 = \pi {\left( {\frac{{{v^2}}}{g}} \right)^2} = \frac{{\pi {v^4}}}{{{g^2}}}$
For maximum area, $r = {R_{\max }} = \frac{{{v^2}}}{g} [{\rm{when }} \theta \,\, = 45^\circ ]$
Maximum area $\pi \;R_{\max }^2 = \pi {\left( {\frac{{{v^2}}}{g}} \right)^2} = \frac{{\pi {v^4}}}{{{g^2}}}$
Standard 11
Physics
