Two bodies are projected with the same velocity. If one is projected at an angle of $30^\circ$ and the other at $45^\circ$ to the horizontal, then the ratio of maximum heights attained is

The path of a projectile in the absence of air drag is shown in the figure by a dotted line. If air resistance is not ignored,then which one of the paths shown in the figure is appropriate for the projectile?

An object is projected with a velocity of $20 \ m/s$ making an angle of $45^{\circ}$ with the horizontal. The equation for the trajectory is $h = Ax - Bx^2$, where $h$ is the height, $x$ is the horizontal distance, and $A$ and $B$ are constants. The ratio $A:B$ is $(g = 10 \ m/s^2)$.

$A$ ball is projected with kinetic energy $E$ at an angle of $45^\circ$ to the horizontal. At the highest point during its flight,its kinetic energy will be

$A$ stone is projected at an angle $\theta$ with velocity $u$. If it executes nearly a circular motion at its maximum point for a short time,the radius of the circular path will be ($g=$ acceleration due to gravity).

$A$ ball rolls off the top of a stairway with horizontal velocity $u$. The steps are $0.1 \ m$ high and $0.1 \ m$ wide. The minimum velocity $u$ with which the ball just hits the $5^{\text{th}}$ step of the stairway will be $\sqrt{x} \ ms^{-1}$ where $x=$ . . . . . . [use $g=10 \ ms^{-2}$].