A unique transport system is built between two stations \(1 \mathrm{~km}\) apart on the surface of the moon. A tunnel in the shape of a full cycloid cycle is dug, and the tunnel is lined with a frictionless material. If mail is dropped into the tube at one station, how much later (in seconds) does it appear at the other station? How deep is the lowest point of the tunnel? (Gravity on the moon is about \(1 / 6\) th that on earth.)