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Q.
A bullet is to be fired with a speed of 2000$\,m{{s}^{-1}} $ to hit a target $200\,m$ away on a level ground. If $ g=10\text{ }m{{s}^{-2}}, $ the gun should be aimed
Horizontal distance of target is 200 m.
Speed of bullet $ =2000\text{ }m{{s}^{-1}} $ .
Time taken by bullet to cover the horizontal distance
$ t=\frac{200}{2000}=\frac{1}{10}s $
During $ \frac{1}{10} $ s,
the bullet will fall down vertically due to gravitational acceleration. Therefore, height above the target, so that the bullet hits the target is
$ h=ut+\frac{1}{2}g{{t}^{2}}=\left( 0\times \frac{1}{10} \right)+\frac{1}{2}\times 10\times {{(0.1)}^{2}} $
$ =0.05\,m=5\,cm $