Two objects are projected with same velocity '$u$' at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha + \beta = 90^{\circ}$, the ratio of horizontal range of the first object to the second object will be $[\sin(\pi - \theta) = \sin \theta]$

$A$ particle of mass $m$ is thrown with an initial speed $u$ at an angle $\theta$ with the horizontal. Find the torque of its weight about the point of projection when it reaches the highest point.

$A$ gun and a target are at the same horizontal level separated by a distance of $600 \,m$. The bullet is fired from the gun with a velocity of $500 \,ms^{-1}$. In order to hit the target, the gun should be aimed to a height $h$ above the target. The value of $h$ is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $\,m$)

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:

$A$ particle is projected at $60^\circ$ to the horizontal with a kinetic energy $K$. The kinetic energy at the highest point is

$A$ stone projected from the ground with a velocity $50 \ m/s$ at an angle of $30^{\circ}$ with the horizontal crosses a wall after a time of $3 \ s$. Then the horizontal distance beyond the wall that the stone strikes the ground is (acceleration due to gravity $g = 10 \ m/s^2$) (in $m$)