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) . At what angle with the vertical should the gun be fired so as to hit the plane ?

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

A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 kmh^(-1) passes directly over head an anti-aircraft gun. At what angle from the vertical should the gun be fired from the shell with muzzle speed 600 ms^(-1) to hit plane. At what minimum altitude should the pilot fly the plane to avoid being hit ? ( Take g= 10 ms^(-2) ).

Consider a shell that has a muzzle velocity of 45ms^(-1) fired from the tail gun of an airplane moving horizontally with a velocity of 215 ms^(-1) . The tail gun can be directed at any angle with the vertical in the plane of motion of the airplane. The shell is fired when the plane is above point A on ground, and the plane is above point B on ground when the shell hits the ground. (Assume for simplicity that the Earth is flat)

A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 kmh^(-1) passes directly over head an anticraft gun. At what angle from the vertical should the gun be fired from the shell with muzzle speed 600 ms^(-1) to hit plane. At what minimum altitude should the pilot fly the plane to avoid being hit ? ( Take g= 10 ms^(-2) ).

A projectile is fired with velocity v_0 from a gun adjusted for a maximum range. It passes through two points P and Q whose heights above the horizontal are h each. Show that the separation of the two points is (v_0)/(g) sqrt(v_0^2 - 4 gh)) .

The maximum range of a gun on horizontal terrain is 1km. If g = 10 ms^(-2) , what must be the muzzle velocity of the shell ?

An artillary piece which consistently shoots its shells with the same muzzle speed has a maximum range R. To hit a target which is R//2 from the gun and on the same level, the elevation angle of the gun should be

A particles is projected horizontally with a speed v from the top of a plane inclined at an angle tehta to the horizontal as shown in the figure. (a) Hwo far from the point of projection will the particle strike the plane ? (b) Find the time taken by the particel to hit the plane. (c) What is the velocity of particle just before it hits the plane ?

A bomb is dropped from an aeroplane when it is at a height h directly above a target. If the aeroplane is moving horizontally at a speed v, the distance by which the bomb will miss the target is given by