# Extra Credit Project: Building the side-track

This project must be done by individuals. You must hand in a printed copy of your work to me by the scheduled time, or place it in the mailbox outside my office door.

You are in charge of designing a small portion of a long train track. In the middle of this region is a train station. There is a single track running away to the East of the station, and a single track running away to the West. Trains will be running in both directions, East and West, throughout the day. If an East-bound train runs into a West-bound train, of course, there will be a big crash.

Your job is to prevent crashes by adding a "side-track" around the station. If two trains approach the station from opposite directions, one can go onto the side-track while the other passes the station, then return to the main track when the coast is clear.

Each train is exactly L = 100 m long, and all trains run at v = 0.9c. Thanks to a sophisticated control system, you can arrange the schedule of the trains so that they will pass each other at any particular point along this section of the track.

Your supervisor says, "Our budget is nearly empty. You need to design the very shortest possible piece of side-track which will just barely allow trains to pass each other without crashing."

How long must the side-track be?

1. Head of the West-bound train reaches the beginning of the side-track.
2. Head of the West-bound train reaches the end of the side-track.
3. Tail of the West-bound train reaches the beginning of the side-track.
4. Tail of the West-bound train reaches the end of the side-track.

In order for no crash to occur, the West-bound and East-bound trains must never touch. Compute the locations of both ends of each train at the times of all 4 events listed above, and verify that no crash occurs.