RPLS Mathematics and Geodesy 3 — Questions and Answers
Question 1: In State Plane Coordinate (SPC) systems, which projection is used for zones that are taller (north-south) than they are wide?
- Transverse Mercator (Correct answer)
- Lambert Conformal Conic
- Albers Equal Area
- Stereographic
Correct answer: Transverse Mercator
Transverse Mercator projection is used for SPC zones elongated in the north-south direction, such as those in narrow states.
Question 2: What is the arc length (s) of a simple circular curve given a radius of 500 ft and a central angle (Δ) of 30°?
- 261.80 ft (Correct answer)
- 250.00 ft
- 523.60 ft
- 125.66 ft
Correct answer: 261.80 ft
s = R × Δ(radians) = 500 × (30 × π/180) = 500 × 0.5236 = 261.80 ft.
Question 3: A level rod reading taken with an automatic level is 4.872 ft. The HI is 105.234 ft. What is the elevation of the rod point?
- 100.362 ft (Correct answer)
- 110.106 ft
- 105.234 ft
- 104.749 ft
Correct answer: 100.362 ft
Elevation = HI − rod reading = 105.234 − 4.872 = 100.362 ft.
Question 4: Which type of error is introduced when a surveyor consistently reads a micrometer one division too high on every observation?
- Systematic error (Correct answer)
- Random error
- Gross error
- Compensating error
Correct answer: Systematic error
Systematic errors follow a predictable pattern and cannot be removed by averaging; they require calibration or correction procedures.
Question 5: In a geodetic context, the 'prime vertical' is the plane that passes through an observer and is oriented in which direction?
- East-west through the zenith and nadir (Correct answer)
- North-south through the zenith and nadir
- Parallel to the equator
- Perpendicular to the geoid
Correct answer: East-west through the zenith and nadir
The prime vertical is the vertical plane through the observer oriented east-west, perpendicular to the meridian plane.
Question 6: Given a bearing of S 42°17'30" W, what is the equivalent azimuth?
- 222°17'30" (Correct answer)
- 137°42'30"
- 42°17'30"
- 317°42'30"
Correct answer: 222°17'30"
S 42°17'30" W is in the third quadrant: azimuth = 180° + 42°17'30" = 222°17'30".
Question 7: The distance distortion factor in a State Plane projection compared to ground distance is known as the:
- Scale factor (k) (Correct answer)
- Grid factor
- Sea-level correction factor
- Elevation factor
Correct answer: Scale factor (k)
The scale factor k describes how grid distances on the SPC map relate to geodetic distances on the ellipsoid at a given location.
RPLS Mathematics and Geodesy 3
In State Plane Coordinate (SPC) systems, which projection is used for zones that are taller (north-south) than they are wide?