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(A) The maximum horizontal range $R$ of a projectile fired with speed $v$ is given by $R = \frac{v^2}{g}$.Since the bullets are fired in all possible

Vedclass · Accepted Answer

$1:16$

Vedclass · Answer

(A) The maximum horizontal range $R$ of a projectile fired with speed $v$ is given by $R = \frac{v^2}{g}$.Since the bullets are fired in all possible directions,the area $A$ covered on the ground is a circle with radius $R$.Thus,the area $A = \pi R^2 = \pi \left( \frac{v^2}{g} \right)^2 = \frac{\pi v^4}{g^2}$.This implies that the area $A \propto v^4$.Given speeds are $v_A = 1 \ km/s$ and $v_B = 2 \ km/s$.The ratio of the areas is $\frac{A_A}{A_B} = \left( \frac{v_A}{v_B} \right)^4 = \left( \frac{1}{2} \right)^4 = \frac{1}{16}$.Therefore,the ratio is $1:16$.

Two guns $A$ and $B$ can fire bullets at speeds $1 \ km/s$ and $2 \ km/s$ respectively. From a point on a horizontal ground,they are fired in all possible directions. The ratio of the maximum areas covered by the bullets fired by the two guns on the ground is

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