A gun can shoot a bullet upto a maximum horizontal range R .If the target is at a horizontal distance `(sqrt(3)R)/2`, at what elevation angle the gun should be held to hit the target?

If the time of flight of a bullet over a horizontal range R is T, then the angle of projection with horizontal is -

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 jet aeroplane is flying at a constant height of 2 km with a speed 360 kmh^(-1) above the ground towards a target and releases a bomb. After how much time it will hit the target and what will be the horizontal distance of the aeroplane from the target so that the bomb should hit the target ? (Take g = 10 ms^(-2))

It was calculated that a shell when fired from a gun with a certain velocity and at an angle of elevation 5pi//36 radius should strike a given target. In actual practice it was found that a hill just intervened in the trajectory. At what angle of elevation should the gun be fired to hit the target ?

A target situated on a hill can be seen from the foot at angle alpha above the horizontal .The distance of the target along the horizonal is R. if a shell is fired from the foot at an angle beta with the horizontal, find the velocity required for it to strike the target.

The childern are trying to shoot a marble into a marble into a small box using a spring loaded gun that fixed on a table and shoots horizontally from the edge of the table. The centre of the box is a horizontal distance 5m from the edge of the table. The first child compresses the spring a distance 2cm and finds that the marble falls short of its target by a horizontal distance 3m . By what distance x should the second child compress the spring to score a direct hit on the box?