Applied Mathematics, Surveying, Principles a. 3.58 m b. 2.

34 m Problem 10:
of Transportation and Highway Engineering, c. 5.32 m d. 1.22 m A student was asked to make a 365.24m
Construction Management, and Methods Problem 6: long line using a 25m tape that is
Subject: 601 Quiz 5 Find the error of line of sight. 0.0024m too long. What is the required
SITUATION 1: (For Problem 1 - 2) A 50 a. -0.0421m b. -0.07665m measured measurement?
m steel tape was standardized and c. -0.0267m d. -0.0995m a. 365.205 m b. 365.152 m
supported throughout its whole length Problem 7: c. 365.458 m d. 365.275 m
and found to be 0.00329 m longer at an Problem 11:
observed temperature of 41.6°C and a Distance Measurements
Find the farthest distance that a man
pull of 12 kilos. This tape was used to aboard the Titanic(whose eye level is 6m
520.14 1
measure a line that was found to be above the waterline) can go so that a
683.21 m at average temperature of 520.20 3 lighthouse 50m high will still be
49.8°C at the same pull. Coefficient of visible(at least the top is visible)?
linear expansion is 0.0000116 m per m. 520.18 6 a. 36.62km b. 35.12km
degree centigrade. c. 37.91km d. 38.87km
Problem 1: 520.24 8 Problem 12:
Determine the standard temperature. The top of a mast signal 2000m away
a. 50.76° b. 35.93° Determine the most probable value of
was sighted through a transit with
c. 44.63° d. 58.34° the tabulated measurements shown:
recorded vertical angle of 4°10’. The
Problem 2: a. 520.208 b. 520.305
height of the mast is 6m and the height
What is the correct length of the line? c. 520.276 d. 520.222
of the transit above the point where it is
a. 683.32m b. 663.28m Problem 8:
set is 1.5m. The elevation of the base of
c. 638.62m d. 633.86m Three groups measured distance AB
the signal B is 175.39m. Compute the
SITUATION 2: (For Problems 3- 4) Find with their respective probable errors.
elevation of the point under transit A
the farthest distance that a man aboard Average Probable with the allowance of curvature and
the Titanic (whose eye level is 6m. above Distance Errors refraction correction formula using
the water line) can go so that a formula h=0.067k2.
lighthouse 50m. high will still be visible. Group A 1234.54 0.3 a. 30m b. 35.214m
Problem 3: c. 32.143m d. 33.922m
Find the distance needed from Situation Group B 1234.67 0.2 Problem 13:
5 in kilometers (km). A sight is taken with an engineers level
a. 36.65 b. 33.51 Group C 1234.59 0.15 at 100m away and an initial reading of
c. 36.77 d. 31.25 Find the most probable value of distance 1.93 is observed. The bubble is then
Problem 4: AB. levelled through five spaces on the level
From Situation 2, what if 2m. allowance a. 1234.712 b. 1234.321 tube when the rod reading is 2.010m.
for tides/waves will be provided, find the c. 1234.607 d. 1234.812 What is the sensitiveness of the level
distance that he can reach. Problem 9: tube in second arc?
a. 26.67 b. 7.7 The difference in elevation between BM1 a. 32.4’’arc/division
c. 33.15 d. 34.37 and BM2 was taken by a survey party b. 33.5’’arc +/division
Problem 5: using three different trials taking c. 30.9’’arc/division
The peg method was conducted and the different paths. d. 31.5’’arc/division
results were as follows: Problem 14:
Difference in Distances A distance was measured on an 8%
Intrument Intrument Elevation
@A @B slope and found to be 2528.75m. What
is the horizontal distance measured in
Group A 34.54 3km
Rod 1.203 0.324 meters?
Reading @ Group B 35.67 4.6km a. 2589.232 b. 2557.251
A c. 2520.697 d. 2522.669
Group C 34.59 3.5km Problem 15:
Rod 2.523 1.445 A 5-meter triangulation observation
Reading @ Find the elevation of BM2 if the elevation tower is on top of hill B 925m above sea
B of BM1 is 105.67. BM1 is lower than level. What would be the height of equal
BM2. towers to be erected at A and C located
Find the difference in elevation between a. 140.76 b. 141.59
A and B. 15km from B respectively if the
c. 141.23 d. 140.52 elevations of A is 960m and that of C is
900m in order that transreceivers at A, A 50m tape was used to measure a line.
B and C will be intervisible? The adjusted distance of the line is
Hcr=0.067k2 120.23m long. If the tape is 0.04m too
a. 15.08 b. 14.75 long. What is the measured distance?
c. 14.21 d. 13.65 a. 120.134 b. 120.270
Problem 16: c. 120.190 d. 120.326
A distance measured with a 50m steel Problem 23:
tape is recorded as 685.24m. The tape is With the transit at point B and line of
known to be 0.014m too long. What is sight horizontal, the stadia intercept at
the correct length of the line in meters? C is 1.25m. If the stadia interval factor
a. 685.124 b. 685.432 is 100.42 and the stadia constant is 0.3,
c. 685.924 d. 685.048 find the distance BC.
a. 122.587 b. 125.825
Problem 17: c. 119.252 d. 128.155
A 50m tape weighing 1.075kg has a Problem 24:
standard pull of 8kg. The tape’s cross- A 2m subtense bar is used to measure
sectional area and modulus of elasticity the distance from A to B. If the angle
are 0.05𝑐𝑚2 and 200 GPa, respectively. subtended by the bar is 5°, find the
What pull (normal tension) is required in distance from A to B.
order that the effect of sag will be a. 22.51 b. 22.15
eliminated when the tape is supported at c. 22.90 d. 22.11
the end point? Problem 25:
a. 214.8 N b. 145.8 N Transit is set up at A observes a stadia
c. 163.5 N d. 197.4 N intercept of 2.2 m at a vertical angle of
Problem 18: +18°23’. The stadia interval factor of the
The observed compass bearing of a line instrument used is 95.5 and stadia
in 1981 was S37°30’E and the magnetic constant of 0.3 m. If the height of the
declination of the place then was known instrument is 1.62 m, and the rod
to be 3°10W. It has also discovered that reading is 1.95 m. Determine the
during the observation local attractions horizontal distance from the transit set
of the place at that moment was 5°E. up at A to the rod at point B
Find the true azimuth of the line. a. 189.48 b. 198.42
a. 322°10’ b. 321°30’ c. 201.43 d. 211.53
c. 324°20’ d. 326°50’
Problem 19:
A 45m course XY, on a level ground was
paced by a surveyor for the purpose of
determining his factor. The number
paces for each trial taken shown in the
accompanying tabulation (51, 53, 52,
53, 50 and 53 paces for 45m) If the
surveyor then took 571,570,568, 570 ,
572, 569 paces in walking an unknown
distance AB. Determine the length of
line.
a. 481.5 b. 465.87
c. 472.24 d. 493.278
Problem 20:
Find the relative precision of the above
situation.
a. 0.00125 b. 0.00641
c. 0.00231 d. 0.00456
Problem 21:
A sight is taken with an engineers level
at 100m away and an initial reading of
1.93 is observed. The bubble is then
levelled through five spaces on the level
tube when the rod reading is 2.010m.
What is the radius of curvature?
a. 4.23m b. 3.75m
c. 3.33m d. 4.56m
Problem 22:
Answer key

1. b
2. a
3. a
4. d
5. d
6. d
7. a
8. c
9. d
10. a
11. a
12. d
13. a
14. c
15. a
16. b
17. d
18. c
19. d
20. a
21. b
22. a
23. b
24. c
25. a