The force of gravity and acceleration going down is the same at both heights, but the acceleration (deceleration) and force from the ground stopping the object isn’t. That second force depends on how fast the object was going, what it’s made of, and what the ground is made of.
The object dropped from twice the height has twice the speed, and an impact with the ground has a limited distance (at most the size of the object if it’s not denting the ground) to stop the object, which means that the faster object is going to experience more force.
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