The range R of projectile is same when its maximum heights are h₁ and h₂. What is the relation between R, h₁ and h₂ ?

Range is same for angles of projection $\theta \text{ and }{90}^{\circ }-\theta .$

$\therefore \mathrm{R}=\frac{{\mathrm{u}}^2\sin 2\mathrm{\theta }}{\mathrm{g}};{\mathrm{h}}_1=\frac{{\mathrm{u}}^2{\sin }^2\mathrm{\theta }}{2\mathrm{g}}$

$\text{ and }{\mathrm{h}}_2=\frac{{\mathrm{u}}^2{\cos }^2\mathrm{\theta }}{2\mathrm{g}}$

$\text{ Hence, }\sqrt{{\mathrm{h}}_1{\mathrm{h}}_2}=\frac{{\mathrm{u}}^2\sin \mathrm{\theta cos}\mathrm{\theta }}{2\mathrm{g}}$