The roof of a tunnel is in the shape of a parabolic arch whose highest point is 18m above the road. The road surface is 16m wide. Lights are placed in the tunnel 12 meters high. How far from center of the tunnel are the lights placed?
To find the distance from the center of the tunnel to where the lights are placed, we can use the concept of symmetry in a parabolic arch.
The highest point of the arch is known to be 18 meters above the road. This means that the vertex of the parabola is at a height of 18 meters.
We also know that the road surface is 16 meters wide. Since a parabola is symmetric, the distance from the center of the tunnel to the edge of the road is half of this width, which is 8 meters.
Since the vertex is 18 meters above the road and the lights are placed at a height of 12 meters, we can find the distance from the center to the lights by subtracting the height of the lights from the height of the vertex:
Distance from center to lights = 18 meters - 12 meters = 6 meters.
Therefore, the lights are placed 6 meters away from the center of the tunnel.