A body is projected from the ground at an angle of $\tan ^{-1}(\sqrt{7})$ with the horizontal. At half of the maximum height, the speed of the body is $n$ times the speed of projection. The value of $n$ is

A cannon placed on a cliff at a height of 375 m fires a cannon ball with a velocity of $100 \mathrm{~ms}^{-1}$ at an angle of $30^{\circ}$ above the horizontal. The horizontal distance between the cannon and the target is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A body $P$ is projected at an angle of $30^{\circ}$ with the horizontal and another body $Q$ is projected at an angle of $30^{\circ}$ with the vertical. If the ratio of the horizontal ranges of the bodies $P$ and $Q$ is $1: 2$, then the ratio of the maximum heights reached by the bodies $P$ and $Q$ is

A projectile is given an initial velocity of $\hat{\mathbf{i}}+2 \hat{\mathbf{j}} \mathrm{~ms}^{-1}$. The cartesian equation of its path is ( $x$ and $y$ are in metres and $g=10 \mathrm{~ms}^{-1}$ )