A bullet is fired with a speed of $$1500\,m/s$$   in order to hit a target $$100\,m$$  away. If $$g = 10\,m/{s^2}.$$   The gun should be aimed

Solution :
The bullet performs a horizontal journey of $$100\,cm$$  with constant velocity of $$1500\,m/s.$$   The bullet also performs a vertical journey of $$h$$ with zero initial velocity and downward acceleration $$g.$$
$$\therefore $$ For horizontal journey, time $$\left( t \right) = \frac{{{\text{Distance}}}}{{{\text{Velocity}}}}$$
$$\therefore t = \frac{{100}}{{1500}} = \frac{1}{{15}}\sec \,......\left( 1 \right)$$
The bullet performs vertical journey for this time.
For vertical journey, $$h = ut + \frac{1}{2}g{t^2}$$
$$\eqalign{ & h = 0 + \frac{1}{2} \times 10 \times {\left( {\frac{1}{{15}}} \right)^2} \cr & {\text{or,}}\,\,h = \frac{{20}}{9}cm = 2.2\,cm \cr} $$