$A$ cricket ball is hit at $30^{\circ}$ with the horizontal with kinetic energy $K$. The kinetic energy at the highest point is

The ratio of the speed of a projectile at the point of projection to the speed at the top of its trajectory is $x$. The angle of projection with the horizontal is

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 $y = (8t - 5t^2) \ m$ and $x = 6t \ m$,where $t$ is in seconds. The velocity with which the projectile is projected is ......... $m/s$.

Two guns $A$ and $B$ can fire bullets at speeds $1 \ km/s$ and $2 \ km/s$ respectively. From a point on a horizontal ground,they are fired in all possible directions. The ratio of the maximum areas covered by the bullets fired by the two guns on the ground is

The angle of projection at which the horizontal range and maximum height of a projectile are equal is

$A$ boy can throw a stone up to a maximum height of $10 \ m$. The maximum horizontal distance that the boy can throw the same stone up to will be .......... $m$.