Final answer:
Both Ball A and Ball B will hit the ground at the same time because they start from the same height with the same speed, in the absence of air resistance.
Step-by-step explanation:
When Ball A is thrown vertically upward from the building, it must come to a stop momentarily at its highest point before coming back down. Only after this will it pass the edge again with the same speed it was thrown but in the opposite direction. Since Ball B is thrown downward from the building at the same instant Ball A passes the edge on the way down, both balls are now effectively in free fall from the same height above the ground and with the same initial speed.
Because the time taken for an object to fall a certain distance only depends on its initial speed and the height to fall, and given that air resistance is neglected, both Ball A and Ball B will take the same amount of time to hit the ground. Therefore, the correct answer is (b), the two balls hit the ground at the same time.