A projectile is launched with velocity $v$ at an angle $heta$ to the horizontal. At the highest point of its trajectory, it explodes into two equal fragments. One fragment falls vertically downwards with zero initial speed. What is the distance from the point of projection where the other fragment lands?

The maximum height attained by a projectile when thrown at an angle $heta$ with the horizontal is found to be half the horizontal range. Then $heta$ is equal to

A man desires to swim across a river through shortest distance the velocity of river water is $3\,Km\,{h^{ - 1}}$. He can swim in still water at $6Km\,{h^{ - 1}}$. At what angle with the velocity of flow of river should he swim?

If two projectiles are launched with the same initial speed but at angles of 30° and 60° with the horizontal, which one will have a greater range (neglecting air resistance)?

A body sitting on the topmost berth in the compartment of a train which is just going to stop on a railway station, drops an apple aiming at the open hand of his brother sitting vertically below his hands at a distance of about 2 m. The apple will fall

A steam boat goes across a lake and comes back (i) on a quiet day when the water is still and (ii) on a rough day when there is a uniform current so as to help the journey onwards and to impede the journey back. If the speed of the launch on both days was same, the time required for complete journey on the rough day, as compared to the quiet day will be

For an object thrown at ${45^0}$ to horizontal, the maximum height (H) and horizontal range (R ) are related as

A stone is projected from the ground with velocity $50{\rm{\;m}}{{\rm{s}}^{ - 1}}$ and angle of ${30^0}$. It crosses a wall after 3 s. How far beyond the wall the stone will strike the ground?

When an object is shot from the bottom of a long smooth inclined plane kept at an angle ${60^{\rm{o}}}$ with horizontal, it can travel a distance ${x_1}$ along the plane. But when the inclination is decreased to ${30^{\rm{o}}}$ and the same object is shot with the velocity, it can travel ${x_2}$ distance. Then ${x_1}:{x_2}$ will be:

A ball is projected with velocity ${v_0}$ at an angle of elevation ${30^0}$. Mark the correct statement

The time of flight of a projectile on an upward inclined plane depends upon