Even though Alzheimer's disease Alzheimer's disease
A neurological disease that affects memory and behaviour. It is characterized by beta-amyloid plaques and neurofibrillary tangles in the brain. There is no known cause but genetics and lifestyle are thought to play a role. is mostly a disorder of memory Memory
The ability to process information that requires attention, storage, and retrieval. and thinking, it can also interfere with a person's mobility Mobility
To be able to move about either on your own or with the use of a walking aid., especially as it progresses. People who have problems with mobility have a higher risk of falling, and falls can be a catastrophe for older people, especially if they break a hip.

I have seen many elderly people who seemed to have been managing reasonably well at home ('maybe a little slowed up') who then have a hip fracture, and never recover their prior mobility or brain function. The previously undetected mild dementia is both a risk for the fall, and a risk for the delirium that comes after the fall.