The physics textbook problem wants the answer “the bullet fired and hit the ground at the same time as the dropped bullet”, since we can neglect air resistance and consider the Earth as flat.
However, in the real life, we should take into account the air resistance. The air resistance provides a drag force which is proportional to the square of the velocity and in the direction opposite to the velocity of the bullet. The vertical component of the air resistance for the fired bullet depends on the velocity of the bullet. That means we can’t treat horizontal motion and vertical motion as independent. Therefore, the fired bullet does not hit the ground at the same time as the dropped bullet, the bullet fired horizontally will take a longer time to fall to the Earth.
MythBusters Bullet Fired Dropped
Image credit: MythBusters | Discovery