Surveying Problems

GERTC – November 2018

Surveying and Transportation Engineering

Situation 1 - The following set of data refers to the amount of money in £s taken by a news vendor for 6 days. {27.90, 34.70, 54.40, 18.92, 47.60, 39.68} 1. Determine the mean values of the set: A. 23.70 B. 27.30 C. 32.70 D. 37.20 2. Determine the median of the set: A. 37.19 B. 31.79 C. 39.71 D. 19.73 3. Determine the modal values of the set: A. 31.20 B. 18.92 C. 34.70 D. no mode 4.

14. Determine the weighted mean for the following angles: 89°42’45”, wt 2; 89°42’42”, wt 1; 89°42’44”, wt 3 A. 89°42’43” B. 89°42’44” C. 89°42’45” D. 89°42’46”

A civil engineer measures a distance between points A and B on the ground. The results came up with five different values. Assuming these values are equally reliable and that the variations result from accidental errors, determine the most probable value of the measured distance. 1 520.62 2 519.92 3 521.63 4 520.98 5 521.02 A. 520.631 B. 520.485 C. 520.834 D. 520.369

5.

A 48 m distance from A to B on a level ground was paced by a civil engineer for the purpose of obtaining his pace factor. From the tabulated data shown, compute the pace factor. Trial Line No. of paces 1 AB 51.0 2 BA 54.0 3 AB 52.5 4 BA 53.0 A. 0.912 B. 0.875 C. 0.792 D. 0.812

6.

A surveying student had recorded the following after repeated pacing: First distance = 100 m No. of paces: 142, 145, 143, 146.5 Second distance = ? No. of paces: 893.5, 896, 891.5, 897 Find the second distance in meters. A. 620 B. 630 C. 640 D. 650

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13. Determine the most probable value based on the number of measurements as tabulated in the table shown below. Distance in meters No. of measurements 520.14 1 520.20 3 520.18 6 520.24 8 A. 520.208 B. 520.20 C. 520.18 D. 520.18

15. Lines of levels are run from bench marks A, B and C to establish elevations at junction point E. The number of set ups per line is observed and the observed elevations of junction E is also tabulated. Route No. of set ups Observed Elevations 1 9 120.48 2 12 120.32 3 4 120.89 Calculated or compute the adjusted elevation of junction E. A. 120.68 m B. 125.28 m C. 110.39 m D. 130.47 m 16. From the following tabulated data, several lines of levels are run over different routes from BM1 to BM2. Determine the most probable value of the difference in elevation between BM1 and BM2. Diff. in Elevation Route Distance Between BM1 and BM2 A 6.32 km. 120.742 B 8.46 km. 120.825 C 10.53 km. 120.863 A. 120.798 B. 120.813 C. 120.762 D. 120.820 17. Lines of level are run from BM1 is 100 m above sea level, determine the most probable value of the elevation of BM2.(BM1 lower than BM2) Route Length (Diff. In Elev.) Between BM1 and BM2 A 10 632.81 B 16 632.67 C 40 633.30 A. 733.38 m B. 743.38 m C. 732.83 m D. 723.83 m

A student recorded the following number of paces after walking a distance of 50 m repeatedly as 71.5, 72.0, 70.0, and 69.5. He wanted to measure the distance between two points C and D. He recorded the following number of paces from C to B or back as 465, 468, 463, and 460. What is the distance from C to D? A. 328 m B. 378 m C. 462 m D. 421 m

8.

A civil engineer recorded 50.8, 52.3, 51.6, and 53.2 paces in walking along a 42 m course to determine his pace factor. He then took 660, 658, 671 and 670 paces in walking an unknown distance AB. Compute the distance AB based on his pace factor. A. 537 m B. 573 m C. 546 m D. 564 m

9.

The frequency distribution given below refers to the heights in centimeters of 100 people. Determine the mean value of the distribution, correct to the nearest millimeter. 150–156 5, 157–163 18, 164–170 20, 171–177 27, 178–184 22, 185–191 8 A. 117.7 cm B. 171.7 cm C. 177.1 cm D. 177.7 cm

18. Line of levels between A and B are run over four different routes. The elevation of A is 640 m with B higher than A. Compute the probable elevation of B. ROUTE DISTANCE (km) DIFF. IN ELEVATION (m) 1 2 0.720 2 4 0.560 3 10 1.080 4 20 0.260 A. 640.69 m B. 679.33 m C. 721.34 m D. 719.20 m 19. Lines of levels are run from station A to station B over three different routes. The route length and difference in elevation between A and B are given in the following table. Route Length (km) Difference in elevation (m) 1 6.2 425.34 2 5.8 424.12 3 3.8 426.45 Determine the most probable value of the elevation of station B if station A is at elevation 187.235 m. A. 613.685 B. 612.3B6 C. 613.125 D. 612.712

10. Four measurements of distance were recorded as 352.45, 352.04, 351.89, and 353.12 meters and given weights of 2, 5, 1, and 8, respectively. Determine the weighted mean. A. 352. 622 B. 352. 863 C. 352.521 D. 353.042

20. The following data are the observed elevation of a point by running a line of levels over four different routes. It is required to determine the most probable value of the elevation. ROUTE ELEVATION PROBABLE ERROR 1 340.22 ±2 2 340.30 ±4 3 340.26 ±6 4 340.32 ±8

11. Suppose four measurements of a distance are recorded as 482.16, 482.17, 482.20, and 482.18 and given weights of 1, 2, 2, and 4, respectively, by the survey-party chief. Determine the weighted mean. A. 428.18 ft B. 482.18 ft C. 438.18 ft D. 483.18 ft 12. Find the weighted mean of the following observations. Route Difference in Weight Elevations A 100.46 1 B 100.50 2 C 100.48 4 A. 100.483 B. 105.398 C. 94.355 D. 110.337

A. 340.261

B. 340.242

C. 340.251

D. 340.293

21. Determine the weighted mean for the following angles: 36°58’32” ±3”; 36°58’28” ±2”; 36°58’26” ±3”; 36°58’30” ±1” A. 36°58’27.51” C. 36°58’29.51” B. 36°58’28.51” D. 36°58’30.51” 1

GERTC – November 2018

Surveying and Transportation Engineering A. ±0.037

22. From the given tabulated data, it is required to determine the most probable value of the elevation of BM2 where lines of levels were run over three different routes with the corresponding probable errors. Route Elevation of BM2 Probable Error A 220.682 ± 0.006 B 220.792 ± 0.012 C 220.846 ± 0.018 A. 220.789 B. 220.802 C. 220.716 D. 220.813

3 B. ±0.073

C. ±0.091

51.75 D. ±0.054

32.From the measured values shown. Find the probable error. TRIALS LENGTH (M) 1 106.87 2 106.90 3 106.93 4 106.89 5 106.81 A. 0.03491 B. 0.09314 C. 0.01349 D. 0.01943

23. Assume the observed angles of a certain plane triangle, and their relative weights, are A = 49°51’15”, Wa = 1; B = 60°32’08”, Wb = 2; and C = 69°36’33”, Wc = 3. Compute the weighted mean of the angles A. 49°51’12”, 60°32’07” and 69°36’41” B. 49°51’20”, 60°32’09” and 69°36’31” C. 49°51’17”, 60°32’09” and 69°36’34” D. 49°51’15”, 60°32’10” and 69°36’35”

33. A line was measured three times and yield the following results: 856.42, 856.69, and 856.12 m. Determine the probable error of the mean. A. ±0.111 m B. ±0.147 m C. ±0.124 m D. ±0.136 m

24. The observed interior angles of a quadrilateral and their corresponding number of observation are as follows: NO. OF CORNER ANGLE OBSERVATIONS 1 67° 5 2 132° 6 3 96° 3 4 68° 4 Determine the corrected angle at corner 4. A. 67°12.63” B. 66°56.84” C. 66°12.38” D. 67°22.63”

Precision 34. The probable error of the mean of 6 observation is 0.043 and the most probable value of the measurement is 860 m Compute the relative precision: 1 1 1 1 A. B. C. D. 20000 10000 8000 36.98 35. A civil engineer measures the distance of points A and B and the following values were recorded in a series of measurements. Determine the relative precision of the measurement. 1 200.58 2 200.40 3 200.38 4 200.46 1 1 1 1 A. B. C. D. 6682 7632 8362 5962

25. From the previous problem. Determine the corrected angle at corner 3. A. 95°37.86’ B. 94°56.84’ C. 95°52.96’ D. 94°12.55’ 26. Two angles AOB and BOC and a single angle AOC are measured at the same point O. Determine the most probable value of angle BOC. ANGLE OBSERVED VALUE NO.OF MEASUREMENTS AOB 33° 46’00” 1 BOC 63° 14’00” 3 AOC 97° 0030” 6 27.The observed angles of a triangle are as follows: A = 34° 20’ 36” B = 49° 16’ 34” C = 96° 22’ 41 Determine the most probable value of angle C: A. 96° 22’44” B. 96° 22’43” C. 96° 22’42” D. 96° 22’40”

PROPAGATION OF ERRORS

28. A , B and C are angles measured from a given triangle .Compute the probable value of angle A : Vertices Hor.Angle No.of measurements A 75° 20’00” 2 B 42° 42’00” 3 C 61° 58’30” 5

37. The base and altitude of a triangle lot were measured to have certain probable errors of 314.60 ± 0.16 and 92.60± 0.14. compute the probable error of the resulting computation.

A. 75° 19’45.48” B.75° 20’36.2 D.75° 19’31.27”

C. 75°

36. The measurement of a base line give a probable length of 2273.656 ± 0.045 later measurements by another party indicate a probable length of 2273.610 ± 0.026 m What is the most probable length of the line obtained by combining results of the two measurements. A. 2273.621 B. 2273.642 C. 2273.659 D. 2273.632

A. ±46.47 B. ±51.98 C. ±36.67 D. ±42.32 1 38. Three measurements of base line given a probable length of 2273.656± 0.045 meters.later measurements by another party indicate a probable length of 2273.610 ± 0.026 m What is the most probable length of the line obtained by combining results of the two measurements? A. 2273.622 B. 2273.631 C. 2273.641 D. 2273.629

20’21.2”

PROBABLE ERRORS

39. The sides of the triangle are given by the following measurements in meters and the corresponding errors: a = 150.41 ± 0.03 b = 198.64 ± 0.05 c = 201.44 ± 0.04 Determine the most probable error of the perimeter. A. 0.09 m B. 0.12 m C. 0.07 m D. 0.15 m

29. Determine the standard deviation from the mean of the set of numbers: {35, 22, 25, 23, 28, 33, 30} correct to 3 significant figures. A. B. C. D. 30. A line was measured three times and yield the following results, 856.42, 856.69 and 856.12 m. Determine the probable error of the mean. A. ±0.111 B. ±0.124 C. ±0.136 D. ±0.147

40. The following sides of a rectangle and its probable errors are 120.40±0.04 and 360.50±0.08 respectively. Compute the probable error of the sum of the sides(perimeter) of the rectangle.

31. In three trials of measuring a certain distance the following data were recorded. Find the probable error. TRIALS LENGTH(m) 1 51.82 2 51.94

A. ±0.126 2 αβγδθμλπσ° 2

B. ±0.092

C. ±0.162

D. ±0.084

GERTC – November 2018 ±∞∠Σ≠τωϕΩ 41. A. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53.

Surveying and Transportation Engineering 54.

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GERTC – November 2018

Surveying and Transportation Engineering

BookMarks: 𝑒 = 2.718281828459045 π = 3.141592653589793 pi = 3.141592653589793 g = 9.80665 m/s²

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