In the room behind the rocket turret, you can find a clipboard with some details on the 'Advanced Knee Replacement'.
The textures are too low-quality to make out any of the words, but this effectively explains how you've been able to survive such long falls throughout the game.
Guide listing help
Unlike normal walkthroughs, in Nice Game Hints you can select just the puzzle you want hints for. Here are listed the puzzles for "Advanced Knee Replacement" in Portal. The guide you choose only contains information about that puzzle, reducing possible spoilers for other puzzles.
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