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 :

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

Tardigrade Admin · Accepted Answer

R = (u2 sin 2 θ/g) A = π R2 A propto R2 A propto u4 (A1/A2) = (u41/u42) = [(1/2)]4 = (1/16)

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 :

1 : 2

1 : 4

1 : 8

1 : 16

$R = \frac{u ^{2} s i n 2 θ}{g}$
$A = π R^{2}$
$A \propto R^{2}$
$A \propto u^{4}$
$\frac{A _{1}}{A _{2}} = \frac{u _{1}^{4}}{u _{2}^{4}} = [\frac{1}{2}]^{4} = \frac{1}{16}$

Q. Two guns A and B can fire bullets at speeds 1km/s and 2km/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 :