In the equation \( y = -16t^2 + 40 \), \( y \) represents the height (in feet) of the egg protection contraption at time \( t \) seconds after it is dropped. The term \( 40 \) represents the initial height from which the egg is dropped, which indicates the height of the school's roof.
Thus, the correct interpretation of the height of the school’s roof is:
40 feet