$A$ body projected horizontally moves with the same horizontal velocity although it is under the action of the force of gravity,why?

(N/A) The force of gravity acts in the vertically downward direction.
According to Newton's first law of motion,an object continues to move with a constant velocity unless acted upon by an external force in that direction.
Since the force of gravity acts only vertically downwards,there is no force acting in the horizontal direction to change the horizontal velocity.
Therefore,the horizontal component of the velocity remains constant throughout the motion.