A hunter aims his gun at a point between the eyebrows of a monkey sitting on a branch of a tree. Just as he fires, the monkey jumps down. The bullet will

If air resistance is neglected, the vertical acceleration due to gravity is the same for both the bullet and the monkey. When the monkey lets go at the instant the gun is fired, it begins to fall with acceleration g; the bullet, while having an initial horizontal component, also experiences the same downward acceleration and thus falls the same vertical distance in the same time. Because horizontal and vertical motions are independent, the bullet remains on a trajectory that intersects the monkey’s falling position, so it strikes the monkey at the point aimed (between the eyebrows) provided the monkey is within range [1].

Sources

1. [1] https://www.animations.physics.unsw.edu.au/jw/monkey_hunter.html