Table 1 shows data collected from a ray trace traverse survey method between old beacons W6 and H2. Use the…

Question

Table 1 shows data collected from a ray trace traverse survey method between old beacons W6 and H2. Use the data and the datum coordinates in Table 2 to compute: Swing and scale factor; (ii) Corrected bearings and distances for the traverse lines and the final coordinates of the new points.

ScanSolve AI Tutor · Accepted Answer

Huu ni utatuzi wa swali la upimaji wa ardhi linalohusisha njia ya "ray trace traverse" kati ya alama za zamani W6 na H2. Tunahitaji kukokotoa "swing" na "scale factor", kisha marekebisho ya "bearings" na umbali, na hatimaye kuratibu mpya za pointi.

Sehemu (i): Kukokotoa Swing na Scale Factor

Badilisha "bearings" kuwa digrii za desimali na kokotoa mabadiliko ya Northing ( $\Delta N$ ) na Easting ( $\Delta E$ ) kwa kila mstari.
Tunatumia fomula: $\Delta N = D \cos(\text{Bearing})$ na $\Delta E = D \sin(\text{Bearing})$ .
- W6 - TP1:
  
  Bearing: $329^\circ 01' 09'' = 329.019167^\circ$
  
  Umbali: 67.227 m
  
  $\Delta N = 67.227 \cos(329.019167^\circ) = 57.627$ m
  
  $\Delta E = 67.227 \sin(329.019167^\circ) = -34.591$ m
- TP1 - TP2:
  
  Bearing: $06^\circ 22' 43'' = 6.378611^\circ$
  
  Umbali: 99.962 m
  
  $\Delta N = 99.962 \cos(6.378611^\circ) = 99.344$ m
  
  $\Delta E = 99.962 \sin(6.378611^\circ) = 11.095$ m
- TP2 - TP3:
  
  Bearing: $40^\circ 33' 18'' = 40.555000^\circ$
  
  Umbali: 101.759 m
  
  $\Delta N = 101.759 \cos(40.555000^\circ) = 77.325$ m
  
  $\Delta E = 101.759 \sin(40.555000^\circ) = 66.137$ m
- TP3 - TP4:
  
  Bearing: $04^\circ 05' 35'' = 4.093056^\circ$
  
  Umbali: 105.032 m
  
  $\Delta N = 105.032 \cos(4.093056^\circ) = 104.766$ m
  
  $\Delta E = 105.032 \sin(4.093056^\circ) = 7.497$ m
- TP4 - H2:
  
  Bearing: $303^\circ 25' 23'' = 303.423056^\circ$
  
  Umbali: 99.331 m
  
  $\Delta N = 99.331 \cos(303.423056^\circ) = 54.713$ m
  
  $\Delta E = 99.331 \sin(303.423056^\circ) = -82.890$ m
Jumlisha $\Delta N$ na $\Delta E$ zilizopimwa (kutoka W6 hadi H2).
$\Delta N_{obs\_total} = 57.627 + 99.344 + 77.325 + 104.766 + 54.713 = 393.775 \text{ m}$ $\Delta E_{obs\_total} = -34.591 + 11.095 + 66.137 + 7.497 - 82.890 = -32.732 \text{ m}$
Kokotoa $\Delta N$ na $\Delta E$ za datum (kutoka W6 hadi H2) kwa kutumia Jedwali 2.
Kuratibu za W6: $N = -147912.146$ m, $E = -29063.323$ m
Kuratibu za H2: $N = -147518.260$ m, $E = -29096.233$ m
$\Delta N_{datum} = N_{H2} - N_{W6} = -147518.260 - (-147912.146) = 393.886 \text{ m}$ $\Delta E_{datum} = E_{H2} - E_{W6} = -29096.233 - (-29063.323) = -32.910 \text{ m}$
Kokotoa Scale Factor ( $S$ ) na Swing ( $\theta$ ).
Tunatumia fomula:
$S \cos \theta = \frac{\Delta N_{obs\_total} \Delta N_{datum} + \Delta E_{obs\_total} \Delta E_{datum}}{\Delta N_{obs\_total}^2 + \Delta E_{obs\_total}^2}$
$S \sin \theta = \frac{\Delta N_{obs\_total} \Delta E_{datum} - \Delta E_{obs\_total} \Delta N_{datum}}{\Delta N_{obs\_total}^2 + \Delta E_{obs\_total}^2}$

Kwanza, kokotoa denominator:
$\Delta N_{obs\_total}^2 + \Delta E_{obs\_total}^2 = (393.775)^2 + (-32.732)^2 = 155058.420625 + 1071.381924 = 156129.802549$
Kisha, kokotoa nambari za $S \cos \theta$ na $S \sin \theta$ :
$\Delta N_{obs\_total} \Delta N_{datum} + \Delta E_{obs\_total} \Delta E_{datum} = (393.775)(393.886) + (-32.732)(-32.910) = 155099.07805 + 1077.20092 = 156176.27897$ $\Delta N_{obs\_total} \Delta E_{datum} - \Delta E_{obs\_total} \Delta N_{datum} = (393.775)(-32.910) - (-32.732)(393.886) = -12969.87525 - (-12899.78912) = -70.08613$
Sasa, kokotoa $S \cos \theta$ na $S \sin \theta$ :
$S \cos \theta = \frac{156176.27897}{156129.802549} = 1.0003091$ $S \sin \theta = \frac{-70.08613}{156129.802549} = -0.0004489$
Kutoka hapa, tunaweza kupata $S$ na $\theta$ :
$S = \sqrt{(S \cos \theta)^2 + (S \sin \theta)^2} = \sqrt{(1.0003091)^2 + (-0.0004489)^2} = \sqrt{1.0006182 + 0.0000002015} = \sqrt{1.0006184015} = 1.0003091$ $\theta = \operatorname{atan2}(S \sin \theta, S \cos \theta) = \operatorname{atan2}(-0.0004489, 1.0003091) = -0.0004487 \text{ rad} = -0.0257^\circ$
Badilisha $\theta$ kuwa digrii, dakika, sekunde:
$-0.0257^\circ = -0^\circ 01' 32.52''$
- Scale Factor: $\boxed{1.0003091}$
- Swing: $\boxed{-0^\circ 01' 32.52''}$
Sehemu (ii): Corrected Bearings na Distances na Final Coordinates
Rekebisha "bearings" kwa kuongeza "swing" angle.
- W6 - TP1: $329^\circ 01' 09'' - 0^\circ 01' 32.52'' = 328^\circ 59' 36.48''$
- TP1 - TP2: $06^\circ 22' 43'' - 0^\circ 01' 32.52'' = 06^\circ 21' 10.48''$
- TP2 - TP3: $40^\circ 33' 18'' - 0^\circ 01' 32.52'' = 40^\circ 31' 45.48''$
- TP3 - TP4: $04^\circ 05' 35'' - 0^\circ 01' 32.52'' = 04^\circ 04' 02.48''$
- TP4 - H2: $303^\circ 25' 23'' - 0^\circ 01' 32.52'' = 303^\circ 23' 50.48''$
Rekebisha umbali kwa kuzidisha na "scale factor".
- W6 - TP1: $67.227 \times 1.0003091 = 67.248$ m
- TP1 - TP2: $99.962 \times 1.0003091 = 99.993$ m
- TP2 - TP3: $101.759 \times 1.0003091 = 101.790$ m
- TP3 - TP4: $105.032 \times 1.0003091 = 105.064$ m
- TP4 - H2: $99.331 \times 1.0003091 = 99.362$ m
Kokotoa kuratibu za mwisho za pointi mpya.
Anza na kuratibu za W6: $N_{W6} = -147912.146$ m, $E_{W6} = -29063.323$ m.
- TP1:
  
  Bearing: $328^\circ 59' 36.48'' = 328.993467^\circ$
  
  Umbali: 67.248 m
  
  $\Delta N = 67.248 \cos(328.993467^\circ) = 57.650$ m
  
  $\Delta E = 67.248 \sin(328.993467^\circ) = -34.610$ m
  
  $N_{TP1} = -147912.146 + 57.650 = -147854.496$ m
  
  $E_{TP1} = -29063.323 - 34.610 = -29097.933$ m
- TP2:
  
  Bearing: $06^\circ 21' 10.48'' = 6.352911^\circ$
  
  Umbali: 99.993 m
  
  $\Delta N = 99.993 \cos(6.352911^\circ) = 99.366$ m
  
  $\Delta E = 99.993 \sin(6.352911^\circ) = 11.059$ m
  
  $N_{TP2} = -147854.496 + 99.366 = -147755.130$ m
  
  $E_{TP2} = -29097.933 + 11.059 = -29086.874$ m
- TP3:
  
  Bearing: $40^\circ 31' 45.48'' = 40.529300^\circ$
  
  Umbali: 101.790 m
  
  $\Delta N = 101.790 \cos(40.529300^\circ) = 77.369$ m
  
  $\Delta E = 101.790 \sin(40.529300^\circ) = 66.148$ m
  
  $N_{TP3} = -147755.130 + 77.369 = -147677.761$ m
  
  $E_{TP3} = -29086.874 + 66.148 = -29020.726$ m
- TP4:
  
  Bearing: $04^\circ 04' 02.48'' = 4.067356^\circ$
  
  Umbali: 105.064 m
  
  $\Delta N = 105.064 \cos(4.067356^\circ) = 104.799$ m
  
  $\Delta E = 105.064 \sin(4.067356^\circ) = 7.458$ m
  
  $N_{TP4} = -147677.761 + 104.799 = -147572.962$ m
  
  $E_{TP4} = -29020.726 + 7.458 = -29013.268$ m
- H2 (Kukagua):
  
  Bearing: $303^\circ 23' 50.48'' = 303.397356^\circ$
  
  Umbali: 99.362 m
  
  $\Delta N = 99.362 \cos(303.397356^\circ) = 54.719$ m
  
  $\Delta E = 99.362 \sin(303.397356^\circ) = -82.896$ m
  
  $N_{H2} = -147572.962 + 54.719 = -147518.243$ m
  
  $E_{H2} = -29013.268 - 82.896 = -29096.164$ m (Kuratibu za H2 zilizokokotolewa zinalingana kwa karibu na kuratibu za datum, tofauti ndogo zinatokana na kuzungusha namba.)
Muhtasari wa Majibu:
- Corrected Bearings:
  
  W6 - TP1: $\boxed{328^\circ 59' 36.48''}$
  
  TP1 - TP2: $\boxed{06^\circ 21' 10.48''}$
  
  TP2 - TP3: $\boxed{40^\circ 31' 45.48''}$
  
  TP3 - TP4: $\boxed{04^\circ

Table 1 shows data collected from a ray trace traverse survey method between old beacons W6 and H2. Use the data and the datum coordinates in Table 2 to compute: Swing and scale factor; (ii) Corrected bearings and distances for the traverse lines and the final coordinates of the new points.

Step-by-step solution

Badilisha "bearings" kuwa digrii za desimali na kokotoa mabadiliko ya Northing ( $\Delta N$ ) na Easting ( $\Delta E$ ) kwa kila mstari.

Jumlisha $\Delta N$ na $\Delta E$ zilizopimwa (kutoka W6 hadi H2).

Kokotoa $\Delta N$ na $\Delta E$ za datum (kutoka W6 hadi H2) kwa kutumia Jedwali 2.

Kokotoa Scale Factor ( $S$ ) na Swing ( $\theta$ ).

Rekebisha "bearings" kwa kuongeza "swing" angle.

Rekebisha umbali kwa kuzidisha na "scale factor".

Kokotoa kuratibu za mwisho za pointi mpya.

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More Mathematics Questions

Table 1 shows data collected from a ray trace traverse survey method between old beacons W6 and H2. Use the data and the datum coordinates in Table 2 to compute: Swing and scale factor; (ii) Corrected bearings and distances for the traverse lines and the final coordinates of the new points.

Step-by-step solution

Badilisha "bearings" kuwa digrii za desimali na kokotoa mabadiliko ya Northing (ΔN\Delta NΔN) na Easting (ΔE\Delta EΔE) kwa kila mstari.

Jumlisha ΔN\Delta NΔN na ΔE\Delta EΔE zilizopimwa (kutoka W6 hadi H2).

Kokotoa ΔN\Delta NΔN na ΔE\Delta EΔE za datum (kutoka W6 hadi H2) kwa kutumia Jedwali 2.

Kokotoa Scale Factor (SSS) na Swing (θ\thetaθ).

Rekebisha "bearings" kwa kuongeza "swing" angle.

Rekebisha umbali kwa kuzidisha na "scale factor".

Kokotoa kuratibu za mwisho za pointi mpya.

Still stuck on this one?

More Mathematics Questions

Badilisha "bearings" kuwa digrii za desimali na kokotoa mabadiliko ya Northing ( $\Delta N$ ) na Easting ( $\Delta E$ ) kwa kila mstari.

Jumlisha $\Delta N$ na $\Delta E$ zilizopimwa (kutoka W6 hadi H2).

Kokotoa $\Delta N$ na $\Delta E$ za datum (kutoka W6 hadi H2) kwa kutumia Jedwali 2.

Kokotoa Scale Factor ( $S$ ) na Swing ( $\theta$ ).