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

$A$ 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 . . . . . . .

It is possible to project a particle with a given velocity in two possible ways so as to make them pass through a point $P$ at a horizontal distance $r$ from the point of projection. If $t_1$ and $t_2$ are times taken to reach this point in two possible ways,then the product $t_1 t_2$ is proportional to

$A$ missile is fired for maximum range at your town from a place $100 \, km$ away from you. If the missile is first detected at its half-way point,how much warning time will you have? (Take $g = 10 \, m/s^2$)

At what point of a projectile motion are acceleration and velocity perpendicular to each other?

$A$ particle moves in a plane with constant acceleration in a direction different from the initial velocity. The path of the particle will be