$A$ stone is projected with kinetic energy $E$,making an angle $\theta$ with the horizontal. When it reaches its highest point,its kinetic energy is

$A$ body is projected at an angle $\theta$ so that its range is maximum. If $T$ is the time of flight, then the value of maximum range is (acceleration due to gravity $= g$)

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

$A$ stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following:

The height of the ceiling in an auditorium is $30 \ m$. $A$ ball is thrown with a speed of $30 \ m \ s^{-1}$ from the entrance such that it just moves very near to the ceiling without touching it and then it reaches the ground at the end of the auditorium. Then the length of the auditorium is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)

If bullets are fired in all possible directions from the same point with an equal velocity of $10 \,m \,s^{-1}$ and an angle of projection $45^{\circ}$,then the area covered by the bullets on the ground is nearly (Acceleration due to gravity $g = 10 \,m \,s^{-2}$) (in $\,m^2$)