A) \[100\,{{m}^{2}}\]
B) \[250\,{{m}^{2}}\]
C) \[314\,{{m}^{2}}\]
D) \[506.5\text{ }{{m}^{2}}\]
Correct Answer: C
Solution :
: A bullet fired behaves like a projectile. Range of a projectile \[=\frac{{{u}^{2}}\sin 2\theta }{g}\] Maximum range is obtained when\[\theta =45{}^\circ \]. \[{{R}_{\max }}=\frac{{{u}^{2}}}{g}\]. This range becomes the radius of circle while area of circle indicates the maximum area on the ground on which these bullets will spread. Area of circle \[=\pi {{(R)}^{2}}\] \[=\pi {{\left( \frac{{{u}^{2}}}{g} \right)}^{2}}=\frac{3.14\times {{(10)}^{4}}}{{{(10)}^{2}}}=3.14\times 100\] \[=314{{m}^{2}}.\]
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