The equation \( y = -16t^2 + 40 \) represents the height \( y \) of the egg protection contraption as a function of time \( t \), where \( y \) is in feet and \( t \) is in seconds.
The \( y \)-intercept of the equation corresponds to the height of the contraption at \( t = 0 \) (the moment it is dropped). By substituting \( t = 0 \) into the equation, we find:
\[ y = -16(0)^2 + 40 = 40 \]
This indicates that the height of the school's roof is 40 feet.
Therefore, the correct interpretation of the height of the school’s roof is 40 feet.