$A$ ball is projected with kinetic energy $E$, at an angle of $60^{\circ}$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will be:

The path of a projectile is given by the equation $y = ax - bx^2$,where $a$ and $b$ are constants,and $x$ and $y$ are the horizontal and vertical distances of the projectile from the point of projection,respectively. The maximum height attained by the projectile and the angle of projection are respectively:

The velocity of projection of a body is increased by $2 \%$. Other factors remaining unchanged,what will be the percentage change in the maximum height attained? (in $\%$)

$A$ helicopter flying horizontally with a velocity of $288 \ km/h$ drops a bomb. If the line joining the point of dropping the bomb and the point where the bomb hits the ground makes an angle $45^{\circ}$ with the horizontal,then the height at which the bomb was dropped is (Acceleration due to gravity $= 10 \ m/s^2$) (in $m$)

$A$ cannon on a level plane is aimed at an angle $\theta$ above the horizontal and a shell is fired with a muzzle velocity $v_0$ towards a vertical cliff a distance $D$ away. Then the height from the bottom at which the shell strikes the side walls of the cliff is

$A$ particle is projected from point $O$ with velocity $u$ at an angle $\alpha$ with the horizontal. If at point $P$,its velocity is perpendicular to the initial direction of projection,then find the time taken to reach from $O$ to $P$.