Four objects $P, Q, R,$ and $S$ are projected with the same velocity at angles of $15^o, 30^o, 45^o,$ and $60^o$ respectively. Which of these will have the minimum range?

The equation of a projectile is $y = \sqrt{3}x - \frac{x^2}{2}$. The velocity of projection is:

$A$ body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is

$A$ particle is projected from point $O$ with velocity $u$ at an angle $\alpha$ with the horizontal. If at point $P$,its velocity is perpendicular to the initial direction of projection,then find the time taken to reach from $O$ to $P$.

$A$ projectile with speed $50 \ m \ s^{-1}$ is thrown at an angle of $60^{\circ}$ with the horizontal. The maximum height that can be reached is,(acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $m$)

$A$ ball is projected from the ground into the air. At a height of $5 \text{ m}$, its velocity is $\vec{v} = (5 \hat{i} + 5 \hat{j}) \text{ m s}^{-1}$. The maximum height reached by the ball is (Acceleration due to gravity $g = 10 \text{ m s}^{-2}$): (in $\text{ m}$)