There is a sinkhole at the center. To measure its depth, a stone is dropped from above the hole.
The stone starts at one edge above the hole and moves toward the opposite wall with initial horizontal speed V. Its initial vertical velocity is 0. There is no air resistance and gravity is g=10 m/s2. Hence after its vertical velocity is reset to 0, the distance it free-falls in time t is s=21gt2=5t2 where s is in m and t is in s.
The hole has width W. Whenever the stone hits a side wall, its vertical velocity becomes 0 so the fall restarts, and its horizontal speed keeps only 80% of its pre-impact magnitude while its direction reverses. Apart from the instant of impact, the horizontal speed stays constant. The stone is small enough to treat as a point.
Given the true depth D of the hole, compute how many times the stone hits a wall before it reaches depth D.