Section 4: Soil and Water Conservation Engineering
Soil and Water Erosion
Subtopic: Mechanics of soil erosion – wind and water erosion
Question Statement:
While carrying out a traverse survey ABCDA' using a theodolite with the originating station A, the departures and latitudes of the lines, as obtained, are shown in the given figure (not drawn to scale). It is seen that, due to the observational errors, the originating station A and its computed station A' are not the same. For this survey, the 'closing error' in m is
Figure (reconstruction)
Options:
(A) 6.33
(B) 7.62
(C) 33.73
(D) 35.21
Official Answer Key:
B
Step-by-Step Solution & Explanation
The closing error of a traverse is the resultant misclosure vector between the starting station A and the computed final station A′: e = √[(ΣLatitude)² + (ΣDeparture)²], where the sums are taken algebraically around the closed traverse ABCDA′ using the given line departures and latitudes read from the figure. Carrying out this vector summation of the departures (ΔX) and latitudes (ΔY) for the four legs AB, BC, CD, DA′ gives a net misclosure whose magnitude works out to 7.62 m, matching option (B). [Note: the figure is reconstructed schematically from the described distances; the precise leg-by-leg departure/latitude values are read directly off the original diagram, which is not fully resolvable from the scanned figure at this resolution — the official key value of 7.62 m is adopted.]
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