A bullet is to be fired with a speed of 2000 ms^-1 to hit a target 200 m away on a level ground. If g = 10 ms ^-2, the gun should be aimed  

Let t be time taken by the bullet to hit the target.

$$\begin{gathered} \mathrm{Range} \mathrm{of} \mathrm{the} \mathrm{projectile} =200=\frac{{\mathrm{u}}^2\sin 2\mathrm{\theta }}{\mathrm{g}} \\ 200=\frac{{\left(2000\right)}^2}{\mathrm{g}}\sin 2\mathrm{\theta } \\ \sin 2\mathrm{\theta }=\frac{1}{2000} ; \mathrm{\theta }=\frac{1}{4000} \\ \mathrm{tan\theta }=\frac{1}{4000}=\frac{\mathrm{h}}{\mathrm{R}}=\frac{\mathrm{h}}{200} \\ \mathrm{h}=\frac{1}{20}\mathrm{m}=5\mathrm{cm} \end{gathered}$$

$\therefore$   Gun should be aimed 5 cm above the target.