Therefore, the height of the ball's 5th fall is 0.125 meters.
To determine this
Ball Initial Height: 32 meters is the ball's initial height.
The ball rebounds to a quarter of its initial height, or the rebound ratio. This implies that the height of the ball is doubled by 1/4 for each descent.
Height after First Fall: The ball is 32 * (1/4) = 8 meters tall after the first fall.
Height following Second Fall: The ball's height following the second fall is 8 * (1/4) = 2 meters.
Height following Fourth Fall: The ball's height following the fourth fall is equal to 0.5 * (1/4) = 0.125 meters.
Height after Fifth Fall: Consequently, 0.125 meters is the height of the ball's fifth fall.