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Two guns $P$ and $Q$ can fire bullets at speeds $2 \mathrm{~km} / \mathrm{s}$ and $4 \mathrm{~km} / \mathrm{s}$, 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
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Verified Answer
The correct answer is:
$1: 16$
As for the projectile motion, horizontal range,
$$
\begin{array}{ll}
& R=\frac{u^2 \sin 2 \theta}{g} \\
\because & \text { Maximum range }=u^2 / g \\
\because & A=\pi R^2 \\
\therefore & A \propto R^2 \\
\text { i.e., } & A \propto u^4 \\
\therefore & \frac{A_1}{A_2}=\frac{u_1^4}{u_2^4}=\left(\frac{2}{4}\right)^4=\left(\frac{1}{2}\right)^4=\frac{1}{16}
\end{array}
$$
$$
\begin{array}{ll}
& R=\frac{u^2 \sin 2 \theta}{g} \\
\because & \text { Maximum range }=u^2 / g \\
\because & A=\pi R^2 \\
\therefore & A \propto R^2 \\
\text { i.e., } & A \propto u^4 \\
\therefore & \frac{A_1}{A_2}=\frac{u_1^4}{u_2^4}=\left(\frac{2}{4}\right)^4=\left(\frac{1}{2}\right)^4=\frac{1}{16}
\end{array}
$$
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