My professor said that the potential energy of an object is larger the higher off the ground it is when it falls. I asked if there is a limit to that potential energy and she said no. I then asked about terminal velocity. Surely if two completely equal objects are dropped from heights sufficiently high enough for both of them to have reached terminal velocity, the height no longer matters pertaining to the amount of energy released? Whether one was up a mile further than the other, at some point they are both falling at the same rate and thus their potential energy is equal from that point on? In my mind, I then equate it to two equal objects falling at the same speed. They will both impact the ground with the same force, no? Where am I going wrong with this?
Edit: I appreciate the answers, but being a neophyte, I’m still slightly confused about the ultimate answer. My new understanding given the answers provided, is that the energy released by the object that has spent a longer time falling will be greater because it has had more energy gathered in some way due to having more time to heat up the air around it, and thus will actually impact with a greater energy released than the object with less time to fall. Is that correct?