a searchlight is shaped like a paraboloid of revolution. if the light source is located 5 feet from the base along the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?
To determine the depth of the searchlight, we need to find the vertical height (or depth) of the paraboloid.
The equation for a vertical cross-section of a parabola is given by:
y = x^2 / (4f)
Where:
y represents the vertical height,
x represents the horizontal distance from the vertex (half of the opening width),
and f represents the focal length.
In this case, the opening width is given as 8 feet, so x = 4 feet. The light source is located 5 feet from the base, which serves as the focal point.
Plugging these values into the equation:
y = (4)^2 / (4*5)
y = 16 / 20
y = 0.8 feet
Hence, the depth of the searchlight should be approximately 0.8 feet.