?If a surveyor measures differences in elevation when making plans for a highway across

Chapter 11, Problem 37

(choose chapter or problem)

If a surveyor measures differences in elevation when making plans for a highway across a desert, corrections must be made for the curvature of the earth.

(a) If \(R\) is the radius of the earth and \(L\) is the length of the highway, show that the correction is

                                                                   \(C=R \sec (L / R)-R\)

(b) Use a Taylor polynomial to show that

                                                                 \(C \approx \frac{L^{2}}{2 R}+\frac{5 L^{4}}{24 R^{3}}\)

(c) Compare the corrections given by the formulas in parts (a) and (b) for a highway that is 100 km long. (Take the radius of the earth to be 6370 km.)

                        

Equation Transcription:

Text Transcription:

R

L

C=R sec(L/R)-R

C approx L^2/2R + 5L^4/24R^3