The ratio of minimum kinetic energies of two projectiles of same mass is $4: 1$ and the ratio of maximum heights attained by them is $4: 1$. Then the ratio of their ranges is . . . . . . (in $: 1$)

$A$ ball of mass $m$ is thrown vertically upwards. Another ball of mass $2m$ is thrown at an angle $\theta$ with the vertical. Both of them stay in air for the same period of time. The heights attained by the two balls are in the ratio of

$A$ bomb is dropped from an aeroplane moving horizontally at a constant speed. When air resistance is taken into consideration,the bomb

$A$ particle is projected vertically upwards from $O$ with velocity $v$ and a second particle is projected at the same instant from $P$ (at a height $h$ above $O$) with velocity $v$ at an angle of projection $\theta$. The time when the distance between them is minimum is

$A$ shot is fired from a point at a distance of $200 \ m$ from the foot of a tower $100 \ m$ high,such that it just passes over it. The direction of the shot with respect to the horizontal is (in $^{\circ}$)

$A$ body $P$ is projected at an angle of $30^{\circ}$ with the horizontal and another body $Q$ is projected at an angle of $30^{\circ}$ with the vertical. If the ratio of the horizontal ranges of the bodies $P$ and $Q$ is $1: 2$, then the ratio of the maximum heights reached by the bodies $P$ and $Q$ is