Kinematics Question 510

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

Options:

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}} $

Show Answer

Answer:

Correct Answer: B

Solution:

Area in which bullet will spread = $ \pi r^{2} $

For maximum area, $ r={R _{\max }}=\frac{v^{2}}{g}[\text{when }\theta =45{}^\circ ] $

Maximum area $ \pi \ R _{\max }^{2}=\pi {{( \frac{v^{2}}{g} )}^{2}}=\frac{\pi v^{4}}{g^{2}} $



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