Q. 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 :

Solution:

$R = \frac{u^{2} \sin 2 \theta}{g} $
$ A = \pi R^{2} $
$ A \propto R^{2} $
$ A \propto u^{4} $
$ \frac{A_{1}}{A_{2}} = \frac{u^{4}_{1}}{u^{4}_{2}} = \left[\frac{1}{2}\right]^{4} = \frac{1}{16} $

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