Oh by the way fixed-focus and optical zoom don't work together. It's one or the other... but fixed focus is garbage anyways.
Most digital point-and-shoots can actually give you a pretty quick response if you set them to continuous autofocus and enable unfocussed shooting. (The second option will likely result in out-of-focus shots though if the operator doesn't know what she's doing, and the first option cuts down on battery life.) Reponse time is one of the things manufacturers have focussed on recently, so your Mom's opinions may be tainted by old technology.
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