If the horizontal range of a projectile is equal to its maximum height, what is the angle of project

Question

If the horizontal range of a projectile is equal to its maximum height, what is the angle of projection?

Professor PC Thomas Classes · Answer

Range $R = \frac{u^2\sin(2	heta)}{g} = \frac{2u^2\sin	heta\cos	heta}{g}$. Max height $h = \frac{u^2\sin^2	heta}{2g}$. Equating them: $\frac{2u^2\sin	heta\cos	heta}{g} = \frac{u^2\sin^2	heta}{2g} \Rightarrow 2\cos	heta = \frac{\sin	heta}{2} \Rightarrow 	an	heta = 4$.