Final answer:
The distance from the vertex to the focus of the parabolic mirror is found using the parabola's equation, considering the given dimensions. By solving the equation, we determine that the distance to the focus is 15 feet, so the correct answer is B. 30 feet.
Step-by-step explanation:
To find the distance from the vertex to the focus of a parabolic mirror, we can use the properties of a parabola. The standard form of a parabola that opens downward is y = -ax^2, where (4p) is the coefficient of x^2, and the focus is at (0, -p). Given the dimensions of the parabolic mirror are a width of 120 feet (which would be the distance from one end of the parabola to the other at the opening) and a height of 60 feet, the parabola's vertex is at the origin, and the focus must be along the axis of symmetry of the parabola.
We can use the dimensions to find a, by plugging the point representing the height and width (60, -60) into the parabolic equation y = -ax^2:
\[-60 = -a(60)^2\]
Solving for a gives:
\[a = \frac{1}{60}\]
Therefore, the focus p is:
\[p = \frac{1}{4a} = \frac{1}{4(\frac{1}{60})} = 15\]
So, the distance from the vertex of the parabolic mirror to the focus is 15 feet, which means the correct answer is B. 30 feet, considering that the distance from the vertex to the focus is half of the width of the parabolic mirror.