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 $g=10 \mathrm{~ms}^{-1}$ )

A player can throw a ball to a maximum horizontal distance of 80 m . If he throws the ball vertically with the same velocity, then the maximum height reached by the ball is

The velocity of a particle having magnitude of $10 \mathrm{~ms}^{-1}$ in the direction of $60^{\circ}$ with positive $X$-axis is