the numbers here are kinda cancer, the time it will take for the egg to fall to the ground height 1.6m is (-5 + sqrt(1193)/10 which is roughly 2.595398 seconds so, the teacher walking at 2 m/s needs to be at 5.9079664 meters away from the building
The head area the egg can hit isn't a singular point in space but a curved surface. The average male head has about 20cm in length, which means if we assume his location corresponds to the center of the head, he should be hit straight in the forehead (even more so if we assume location at neck area)