An aeroplane flies horizontally at a height h at speed v. An anti - carft gun a shell at the plane when it is vertically above the gun . Show that the minimum muzzle velocity required to hit the plane is `sqrt(v^(2) + 2gh)` at an angle `tan^(-1) ((sqrt(2gh))/(v))` .

An enemy plane is flying horizontally at an altitude of 2 km with a speed of 300 ms^(-1) An army man with an anti-aircraft gun on the ground sights hit enemy plane when it is directly overhead and fires a shell with a muzzle speed of 600 ms^(-1) . Ar what angle with the vertical should the gun be fired so as to hit the plane ?

Show that the semi-vertical angle of right circular cone of the maximum volume and of given slant height is tan^(-1) sqrt(2)