If a ball is dropped from rest from an elevated position at the same instant that a second ball is launched horizontally (from the same height), then which ball will hit the ground first? assume the balls behave as projectiles

Both balls will hit the ground at the same time

Explanation:

After the launch, only gravity acts on the balls. No other force. Gravity causes an acceleration that is same (in magnitude and direction) for all masses. Therefore the balls accelerate downward at the same rate. Since they were launched from same height, there is no reason, either of them should hit the ground before its companion. The only difference will be which spot on the ground - the ball launched horizontally will have moved "sideways" a bit while accelerating down.