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.

A football is kicked with a speed of $22 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle of $60°$ to the positive $x$ direction, taken along the horizontal. At that instant, an observer moves past the football in a car that moves with a constant speed of $11\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ in the positive $x$ direction. Take positive $y$direction vertically upwards.$(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

A particle $P$  is projected from a point on the surface of a smooth inclined plane (see figure). Simultaneously, another particle $Q$ is released on the smooth inclined plane from the same position. $P$ and $Q$ collide after $t=4 \mathrm{s}$. The speed of projection of $P$ is
 

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