Two particles $P$ and $Q$ are projected simultaneously away from each other from a point $A$ as shown in the figure.

The velocity of $P$ relative to $Q$ in $\mathrm{m} {\mathrm{s}}^{-1}$ at the instant when the motion of $P$ is horizontal is

Two guns on a battleship simultaneously fire two shells at the same speed at enemy ships. If the shells follow the parabolic trajectories shown in the figure, which ship will get hit first?

Two identical balls are set into motion simultaneously from equal heights $h$. While the ball $A$ is thrown horizontally with velocity $v$, the ball $B$ is just released to fall by itself. Choose the alternative that best represents the motion of $A$ and $B$ with respect to an observer who moves with the velocity $\frac{v}{2}$ with respect to the ground as shown in the figure.

A shot is fired at an angle $\mathrm{\theta }$ to the horizontal such that it strikes the hill while moving horizontally. Find the initial angle of the projection $\mathrm{\theta }$.

A man is riding on a horse. He is trying to jump the gap between two symmetrical ramps of snow separated by a distance $W$ as shown in the figure. He launches off the first ramp with a speed $V_{\mathrm{L}}$. The man and the horse have a total mass $m$ and their size is small as compared to $W$. The value of initial launch $V_{\mathrm{L}}$ speed which will put the horse exactly at the peak of the second ramp is