Speed of rocks when they hit the ground

[limonade]

Homework Statement

If I throw a rock upwards with an initial velocity and throw a rock downwards, what is the speed of the rocks just before they hit the ground?

Homework Equations

The Attempt at a Solution

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They should hit the ground at the same speed and different times. I would use the conservation of mechanical energy, but someone I'm speaking to disagrees with me that they have same speed.

How would you show this mathematically?

 

[SteamKing]

Use the formulas for objects traveling in a gravity field. You are studying physics, I presume.

 

[nil1996]

See your initial kinetic energy is the final potential energy.
use this relation.