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 maximum areas covered by the bullets fired by the two guns, on the ground is:

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Q.

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

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a

$1 : 8$

b

$1 : 2$

c

$1 : 16$

d

$1 : 4$

answer is A.

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Detailed Solution

$R = \frac{u^{2} \sin 2 θ}{g}$ , For maximum range $θ$ is 45^0.

$A = π R^{2}$

$A \propto u^{4}$

$\frac{A_{1}}{A_{2}} = \frac{u_{1}^{4}}{u_{2}^{4}} = {[\frac{1}{2}]}^{4} = \frac{1}{16}$

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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 maximum areas covered by the bullets fired by the two guns, on the ground is: