The first breakthrough in the description of projectile motion was made by Galileo. He showed that the horizontal and vertical motions of a slow moving projectile are mutually independent.
Suppose a boy throws a ball with an initial horizontal speed. According to Newton’s second law there will be no acceleration in the horizontal direction unless a horizontally directed force acts on the ball. Ignoring friction of air, the only force acting on the ball once it is free from the hand of the boy is the force of gravity.
Hence, the horizontal speed of the ball does not change. But as the ball moves with this speed to the right, it also falls under the action of gravity.