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A number of bullets are fired in all possible directions with the same initial speed $u$ . The maximum area of ground covered by bullets is proportional to $u^{x}$ ,then $x$ is _____.

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answer is 4.

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Detailed Solution

A bullet fired at angle $45^{0}$ will fall maximum away, and all other bullets will fall with this bullet fired at $45^{0}$ . $R_{\max} = \frac{u^{2}}{g}$
maximum area covered $= π {(R_{\max})}^{2} = π {(\frac{u^{2}}{g})}^{2}$

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