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Thank you for using Just Answer. My name is Rebecca; I am a veterinarian. Please give me a moment to type my answer.
I am sorry you are worried about your daughter's cat. It is hard to say what any cat will do! I once heard of a blind Chihuahua would would jump from the upstairs balcony onto the couch!
If he is an active cat, he may jump or fall. Although 9 feet is a long distance, cats have survived much longer falls with few or no injuries. A cat once fell out of a high rise, I forget how many stories, and only broke the tip of his lower jaw that healed well. They do land on their feet!
If he jumps on purpose, he will probably be aiming for a soft landing, such as a piece of furniture. He might even try to jump from the lower level onto the balcony, and he might miss and fall; I have seen cats try to jump up onto the ceiling rafters (again with no injuries). It will really be up to him what he tried to do, but being a cat his fall (if he falls) may not leave him with serious injuries.
Let me know what other questions you have.
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