If a body $A$ of mass $M$ is thrown with velocity $v$ at an angle of $30^{\circ}$ to the horizontal and another body $B$ of the same mass is thrown with the same speed at an angle of $60^{\circ}$ to the horizontal,the ratio of the horizontal range of $A$ to $B$ will be:

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 $= 10 \ m \ s^{-2}$)

Two stones are thrown with the same speed $u$ at different angles from the ground into the air. If both stones have the same range and the heights attained by them are $h_1$ and $h_2$,then $h_1 + h_2$ is equal to .......

At which points of its trajectory will a projectile have minimum and maximum speed?

The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5t^2) \text{ m}$ and $x = 6t \text{ m}$,where $t$ is in seconds. The acceleration due to gravity on this planet is ......... $m/s^2$.

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 $\,m^2$)