Hi, I have no idea about this problem. Could you please help me figure out? Thank you very much.

Q: A particular problem is de-railing due to curving of the tracks. This problem is sometimes also called sun curves, since it is caused by the sun heating the rails. When the rails heat up they expand slightly. When the endpoints are fixed instead of expansion along the track the rail will curve out in a circle segment. Perhaps surprisingly even a small expansion can cause a significant lateral displacement. A particular rail has a base length L=20m. During the day it has expanded with 2mm = 0.002m. Determine the lateral displacement h caused by this. Use Newton's method to solve the problem. How can you find a good starting approximation for h?

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