In projectile motion, why does an object that is vertically dropped down and an object that is horizontally launched reach the ground at the same time?
A dropped object accelerates downward at g. The time to the ground is given by
A projectile launched horizontally accelerates downward at g. The time to the ground is given by
where the vertical component of its velocity,
One condition: if the ground is not perfectly level from the site of the launch of the projectile to the impact area, that would change things.
I hope this helps,