The maximum range of a gun of horizontal terrain is $10 k m$ . If $g = 10 m / s^{2}$ . What must be the muzzle velocity of the shell ?

400 m / s

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200 m / s

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100 m / s

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50 m / s

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Solution

The correct option is (C) $100 m / s$
Let the muzzle velocity of shell be $u$ .
For maximum range, $R = \frac{u^{2}}{g}$
$\Rightarrow u^{2} = g R$
Given : $R = 10 k m = 10000$ m
$u^{2} = 1000 \times 10$
$\Rightarrow u$ $= 100 m / s e c$
Hence, muzzle velocity is $100 m / s$

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