Two guns P and Q can fire bullets at speeds 2 ~km / s and 4 ~km / s , respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum or areas covered by the bullets fired by the two guns, on the ground is

Step-by-step solution

The maximum horizontal range R of a projectile fired with speed v is given by the formula R = v^2 g , where g is the acceleration due to gravity. The bullets are fired in all possible directions, so the area covered on the ground is a circle with radius R . The area A is given by A = R^2 = ( v^2 g )^2 = v^4 g^2 . For gun P , the speed is v_P = 2 km/s . The area covered is A_P = (2)^4 g^2 = 16 g^2 . For gun Q , the speed is v_Q = 4 km/s . The area covered is A_Q = (4)^4 g^2 = 256 g^2 . The ratio of the areas covered