Two spheres are projected at angles $30^\circ$ and $45^\circ$ with the horizontal. The maximum height reached by both is same. The ratio of their initial velocities is, $\left(\sin 45^\circ = \dfrac{1}{\sqrt{2}}, \sin 30^\circ = 0.5\right)$

The equation of the trajectory of a ball projected at an angle $\theta$ with the horizontal, is given as $y = x - \dfrac{gx^2}{2}$
The initial velocity of the ball is
[Given : $\tan 45^\circ = 1$, $\cos 45^\circ = \dfrac{1}{\sqrt{2}}$ ]

For a projectile motion, the range R is 'n' times the maximum height H. So the angle of projection is

A ball P is projected at an angle of $60^\circ$ with the vertical with certain initial speed. Another ball Q of the same mass as that of ball P is projected vertically upwards with the same initial speed as that of P. At the highest point, the ratio of potential energy of ball P to that of ball Q is
$(\sin 30^\circ = 0.5)$