This is not a model taken from Galileo's notes.
But Galileo did show that free falling motion was independent of horizontal motion.
The "Dimension Splitter" gun, A in this picture and photo below, has a horizontal shaft which hits a wood ball.
The wood ball moves horizontally forward and brakes the fine wire contact switch to an
electro-magnet holding a steel ball. The steel ball is released at the same height as the wood ball.
Does the wood projectile hit the floor at the same time as the steel projectile?
Now that you are sure they hit at the same time reconsider the question while considering the speed of sound, around 13,976 inches per second, and your position in the room.
Now reconsider the question while considering the speed of light, around 11,802,852,677 inches per second, and your position in the room.