A boy aims a gun at a bird from a point, at a horizontal distance of 100 m. If the gun can impart a velocity of 500 $m{s}^{-1}$ to the bullet. At what height above the bird must he aim his gun in order to hit it (take g = 10 $m{s}^{-2}$)

Time taken by bullet to travel a horizontal distance of 100 m is given by $t=\frac{100}{500}=\frac{1}{5}sec$_. In this time the bullet also moves downward due to gravity its vertical displacement,$h=\frac{1}{2}g{t}^2=\frac{1}{2}\times 10\times {\left(\frac{1}{5}\right)}^2$$=\frac{1}{2}\times 10\times {\left(\frac{1}{5}\right)}^2$$=1/5m$= 20 cm

So bullet should be fired aiming 20 cm above the bird to hit it.