Hmm, If a stick is traveling at the speed of light (299,792,458 m/s) then I would doubt there would be enought time for it to fall in to the hole in just 1/299,792,458 of a second.
This reminds me of a similiar riddle where two friends reunite after many years and one friend determines the ages of the other's children using the address where they used to play chess and "the youngest one likes pickles."
good riddle.