Question

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 :

• A. 1 : 2
• B. 1 : 4
• C. 1 : 8
• D. 1 : 16

Answer 1

Answer: (D)

$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} $