A stone is projected from a horizontal plane. It attains a maximum height $H$ & strikes a stationary smooth wall & falls on the ground vertically below the maximum height. Assuming the collision to be elastic, the height of the point on the wall, where the ball will strike, is

Two guns are mounted (fixed) on two vertical cliffs that are very high from the ground as shown in figure. The muzzle velocity of the shell from $G_1$ is $u_1$ and that from $G_2$ is $u_2$. The guns aim exactly towards each other. The ratio $u_1:u_2$ such that the shells collide with each other in air is (Assume that there is no resistance of air.)

A stone projected at an angle of $60°$ from the ground level strikes at an angle of $30°$ on the roof of a building of height $h$. The speed of projection of the stone is

An aircraft moving with a speed of $972 \mathrm{km} {\mathrm{h}}^{-1}$ is at a height of $6000 \mathrm{m}$, just overhead of an anti-aircraft gun. The muzzle velocity of the gun is $540 \mathrm{m} {\mathrm{s}}^{-1}$. Find the firing angle $\theta$ for which the bullet hit the aircraft.