A bullet is fired from a gun with a speed of $$1000\,m/s$$   in order to hit a target $$100\,m$$  away. At what height above the target should the gun be aimed? (The resistance of air is negligible and $$g = 10\,m/{s^2}$$  )

Solution :
Horizontal distance of the target is $$100\,m.$$
Speed of bullet $$= 1000\,m/s$$
Time taken by bullet to cover the horizontal distance,
$$t = \frac{{100}}{{1000}} = \frac{1}{{10}}s$$
During $$\frac{1}{{10}}s,$$  the bullet will fall down vertically due to gravitational acceleration.
Therefore, height above the target, so that the bullet hit the target is
$$\eqalign{ & h = ut + \frac{1}{2}g{t^2} = \left( {0 \times \frac{1}{{10}}} \right) + \frac{1}{2} \times 10 \times {\left( {0.1} \right)^2} \cr & = 0.05\,m \cr & = 5\,cm \cr} $$