JEE MAIN - Physics (2019 - 10th January Morning Slot - No. 21)
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 : 16
1 : 8
1 : 2
1 : 4
Explanation
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$$R = {{{u^2}\sin 2\theta } \over g}$$
$$A = \pi \,{R^2}$$
$$A \propto {R^2}$$
$$A \propto {u^4}$$
$${{{A_1}} \over {{A_2}}} = {{u_1^4} \over {u_2^4}} = {\left[ {{1 \over 2}} \right]^4} = {1 \over {16}}$$
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