A projectile can have the same range $$R$$ for two angles of projection. If $${t_1}$$ and $${t_2}$$ be the times of flight in two cases, then what is the product of two times of flight?

Solution :
$$\eqalign{ & {t_1} = \frac{{2u\sin \theta }}{g}\,{\text{and}} \cr & {t_2} = \frac{{2u\sin \left( {90 - \theta } \right)}}{g} \cr & = \frac{{2u\cos \theta }}{g} \cr & \therefore {t_1}{t_2} = \frac{{4{u^2}\cos \theta \sin \theta }}{{{g^2}}} = \frac{2}{g}\left[ {\frac{{{u^2}\sin \theta }}{g}} \right] \cr & = \frac{2}{g}R, \cr} $$
where $$R$$ is the range. Hence $${t_1}{t_2} \propto R$$