Answer:
The professor should be
away of the impact point, walking towards it.
Explanation:
We will calculate how much time an egg takes to fall from the initial position to the final position, and then use that time to calculate how much distance the professor moved.
We use the equation for accelerated motion (on the vertical direction):

Since it departs from rest and the acceleration is that of gravity, we have:

Which means:

Having the ground as reference and taking the upwards direction as positive, for our values we have:

And in that time the professor moved 