You drop a ball from rest and simultaneously shoot a second, identical ball horizontally from the same height as the first ball. If there is no air resistance, which ball hits the ground first?

They would hit the ground at the same time.

Explanation:

Because air resistant is ignored, then gravitational acceleration g is the only thing that affect the both of the balls vertical motion, no matter what their horizontal motion is. Since both balls starts from rest, vertically speaking their speeds are zero initially, so they are both subjected to the same constant gravitational acceleration g, then they travel at the same rate and would reach the ground at the same time.