A plane flying horizontally at a height of $1500 \mathrm{m}$ with a velocity of $200 \mathrm{m} {\mathrm{s}}^{-1}$ passes directly overhead an antiaircraft gun. Then the angle with the horizontal at which the gun should be fired for the shell with a muzzle velocity of $400 \mathrm{m} {\mathrm{s}}^{-1}$ to hit the plane is -

A stone projected at an angle of $60°$ from the ground level strikes at an angle of ${30}^0$ on the roof of a building of height $h$. Then the speed of projection of the stone is:

A projectile is fired at an angle $\theta$ with the horizontal. Find the condition under which it lands perpendicular on an inclined plane of inclination $\alpha$ as shown in the figure.

Three particles$P, Q$ and $R$ are placed as per the given figure. Masses of $P\mathit{,}\mathit{ }Q$ and $R$ are $\sqrt{3 m}, \sqrt{3 m}$ and $m$ respectively. The gravitational force on a fourth particle $S$ of mass $m$ is equal to

The velocity of end $A$ of rigid rod placed between two smooth vertical walls is $u$ along vertical direction. Find out the velocity of end $B$ of that rod, when it slips down.Rod always remains in contact with the vertical wall and also find the velocity of centre of mass of the rod. Also find equation of path of centre of rod.