Question

What is the angle at which both the height and the range of projectile is maximum?

Answer 1

$$R=\frac{v^2}{g}\sin{2\theta}=\frac{v^2}{g}2\sin{\theta}\cos{\theta}$$

$$H=\frac{v^2}{2g}\sin^2{\theta}$$

So,

$$\frac{v^2}{g}2\sin{\theta}\cos{\theta}=\frac{v^2}{2g}\sin^2{\theta}$$

$$\tan{\theta}=4$$

$$\theta=\arctan{4}=76\degree$$