$A$ stone is projected at an angle of $30^{\circ}$ to the horizontal. The ratio of the kinetic energy of the stone at the point of projection to its kinetic energy at the highest point of its flight will be:

$A$ particle is projected from the ground with a speed of $80 \,m/s$ at an angle of $30^{\circ}$ with the horizontal. The magnitude of the average velocity of the particle in the time interval $t=2 \,s$ to $t=6 \,s$ is ....... $m/s$. (Take $g=10 \,m/s^2$)

$A$ body is projected at an angle of $60^{\circ}$ with the horizontal such that the vertical component of its initial velocity is $40 \ m \ s^{-1}$. The magnitude of velocity of the projectile at one quarter of its time of flight is nearly (Acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $m \ s^{-1}$)

$A$ ball $P$ is projected at an angle of $60^{\circ}$ with the vertical with a certain initial speed $u$. Another ball $Q$ of the same mass $m$ as that of ball $P$ is projected vertically upwards with the same initial speed $u$. At the highest point, the ratio of the potential energy of ball $P$ to that of ball $Q$ is $(\sin 30^{\circ} = 0.5)$.

$A$ particle is projected with kinetic energy $K$ at an angle of $60^o$ with the horizontal. The kinetic energy of the particle at the maximum height is . . . . . . .

If $R$ and $H$ represent the horizontal range and the maximum height achieved by a projectile,then which of the following relations exists?