Tunnel Problem: Scorpion Gulch and Western Railway is preparing to build a new line

Chapter 4, Problem 25

(choose chapter or problem)

Tunnel Problem: Scorpion Gulch and Western Railway is preparing to build a new line through Rolling Mountains. They have hired you to do some calculations for tunnels and bridges needed on the line (Figure 4-6k). You set up a Cartesian coordinate system with its origin at the entrance to a tunnel through Bald Mountain. Your surveying crew finds that the mountain rises 250 m above the level of the track and that the next valley goes down 50 m below the level of the track. The cross section of the mountain and valley is roughly sinusoidal, with a horizontal distance of 700 m from the top of the mountain to the bottom of the valley (Figure 4-6k). a. Write a particular equation expressing the vertical distance y, in meters, from the track to the surface of the mountain or valley as a function of x, in meters, from the tunnel entrance. You can find the constants A, B, and C from the given information. Finding the phase displacement D requires that you substitute the other three constants and the coordinates (0, 0) for (x, y), then solve for D. b. How long will the tunnel be? How long will the bridge be? c. The railway company thinks it might be cheaper to build the line if it is raised by 20 m. The tunnel will be shorter, and the bridge will be longer. Find the new values of x at the beginning and end of the tunnel and at the beginning and end of the bridge. How long will each be under these conditions? 2

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back