The maximum height reached by a projectile is $64 \,m$. If the initial velocity is halved, the new maximum height of the projectile is . . . . . . $m$.

$A$ projectile is thrown with velocity $u$ making an angle $\theta$ with the vertical. It just crosses the tops of two poles each of height $h$ after $1\,s$ and $3\,s$,respectively. The maximum height of the projectile is ............ $m$.

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 $\,m^2$)

Two projectiles are projected with the same initial velocities at $15^{\circ}$ and $30^{\circ}$ with respect to the horizontal. The ratio of their ranges is $1 : x$. The value of $x$ is:

$A$ ball is projected in a manner such that its horizontal range is $n$ times the maximum height. Find the ratio of potential energy to kinetic energy at the maximum height.

For a projectile,the ratio of the maximum height reached to the square of the time of flight is: