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.
|Mathematics
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 Answer
Answer
1.0003091
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
Hatua ya 1: Badilisha "bearings" kuwa digrii za desimali na kokotoa mabadiliko ya Northing (ΔN) na Easting (ΔE) kwa kila mstari.
Tunatumia fomula: ΔN=Dcos(Bearing) na ΔE=Dsin(Bearing).
W6 - TP1:
Bearing: 329∘01′09′′=329.019167∘
Umbali: 67.227 m
ΔN=67.227cos(329.019167∘)=57.627 m
ΔE=67.227sin(329.019167∘)=−34.591 m
TP1 - TP2:
Bearing: 06∘22′43′′=6.378611∘
Umbali: 99.962 m
ΔN=99.962cos(6.378611∘)=99.344 m
ΔE=99.962sin(6.378611∘)=11.095 m
TP2 - TP3:
Bearing: 40∘33′18′′=40.555000∘
Umbali: 101.759 m
ΔN=101.759cos(40.555000∘)=77.325 m
ΔE=101.759sin(40.555000∘)=66.137 m
TP3 - TP4:
Bearing: 04∘05′35′′=4.093056∘
Umbali: 105.032 m
ΔN=105.032cos(4.093056∘)=104.766 m
ΔE=105.032sin(4.093056∘)=7.497 m
TP4 - H2:
Bearing: 303∘25′23′′=303.423056∘
Umbali: 99.331 m
ΔN=99.331cos(303.423056∘)=54.713 m
ΔE=99.331sin(303.423056∘)=−82.890 m
Hatua ya 2: Jumlisha ΔN na ΔE zilizopimwa (kutoka W6 hadi H2).ΔNobs_total=57.627+99.344+77.325+104.766+54.713=393.775mΔEobs_total=−34.591+11.095+66.137+7.497−82.890=−32.732m
Hatua ya 3: Kokotoa ΔN na ΔE 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
ΔNdatum=NH2−NW6=−147518.260−(−147912.146)=393.886mΔEdatum=EH2−EW6=−29096.233−(−29063.323)=−32.910m
Hatua ya 4: Kokotoa Scale Factor (S) na Swing (θ).
Tunatumia fomula:
Scosθ=ΔNobs_total2+ΔEobs_total2ΔNobs_totalΔNdatum+ΔEobs_totalΔEdatumSsinθ=ΔNobs_total2+ΔEobs_total2ΔNobs_totalΔEdatum−ΔEobs_totalΔNdatum
Kwanza, kokotoa denominator:
ΔNobs_total2+ΔEobs_total2=(393.775)2+(−32.732)2=155058.420625+1071.381924=156129.802549
Kisha, kokotoa nambari za Scosθ na Ssinθ:
ΔNobs_totalΔNdatum+ΔEobs_totalΔEdatum=(393.775)(393.886)+(−32.732)(−32.910)=155099.07805+1077.20092=156176.27897ΔNobs_totalΔEdatum−ΔEobs_totalΔNdatum=(393.775)(−32.910)−(−32.732)(393.886)=−12969.87525−(−12899.78912)=−70.08613
Sasa, kokotoa Scosθ na Ssinθ:
Scosθ=156129.802549156176.27897=1.0003091Ssinθ=156129.802549−70.08613=−0.0004489
Kutoka hapa, tunaweza kupata S na θ:
S=(Scosθ)2+(Ssinθ)2=(1.0003091)2+(−0.0004489)2=1.0006182+0.0000002015=1.0006184015=1.0003091θ=atan2(Ssinθ,Scosθ)=atan2(−0.0004489,1.0003091)=−0.0004487rad=−0.0257∘
Badilisha θ kuwa digrii, dakika, sekunde:
−0.0257∘=−0∘01′32.52′′
Scale Factor:1.0003091
Swing:−0∘01′32.52′′
Sehemu (ii): Corrected Bearings na Distances na Final Coordinates
Hatua ya 5: Rekebisha "bearings" kwa kuongeza "swing" angle.
W6 - TP1: 329∘01′09′′−0∘01′32.52′′=328∘59′36.48′′
TP1 - TP2: 06∘22′43′′−0∘01′32.52′′=06∘21′10.48′′
TP2 - TP3: 40∘33′18′′−0∘01′32.52′′=40∘31′45.48′′
TP3 - TP4: 04∘05′35′′−0∘01′32.52′′=04∘04′02.48′′
TP4 - H2: 303∘25′23′′−0∘01′32.52′′=303∘23′50.48′′
Hatua ya 6: Rekebisha umbali kwa kuzidisha na "scale factor".
W6 - TP1: 67.227×1.0003091=67.248 m
TP1 - TP2: 99.962×1.0003091=99.993 m
TP2 - TP3: 101.759×1.0003091=101.790 m
TP3 - TP4: 105.032×1.0003091=105.064 m
TP4 - H2: 99.331×1.0003091=99.362 m
Hatua ya 7: Kokotoa kuratibu za mwisho za pointi mpya.
Anza na kuratibu za W6: NW6=−147912.146 m, EW6=−29063.323 m.
TP1:
Bearing: 328∘59′36.48′′=328.993467∘
Umbali: 67.248 m
ΔN=67.248cos(328.993467∘)=57.650 m
ΔE=67.248sin(328.993467∘)=−34.610 m
NTP1=−147912.146+57.650=−147854.496 m
ETP1=−29063.323−34.610=−29097.933 m
TP2:
Bearing: 06∘21′10.48′′=6.352911∘
Umbali: 99.993 m
ΔN=99.993cos(6.352911∘)=99.366 m
ΔE=99.993sin(6.352911∘)=11.059 m
NTP2=−147854.496+99.366=−147755.130 m
ETP2=−29097.933+11.059=−29086.874 m
TP3:
Bearing: 40∘31′45.48′′=40.529300∘
Umbali: 101.790 m
ΔN=101.790cos(40.529300∘)=77.369 m
ΔE=101.790sin(40.529300∘)=66.148 m
NTP3=−147755.130+77.369=−147677.761 m
ETP3=−29086.874+66.148=−29020.726 m
TP4:
Bearing: 04∘04′02.48′′=4.067356∘
Umbali: 105.064 m
ΔN=105.064cos(4.067356∘)=104.799 m
ΔE=105.064sin(4.067356∘)=7.458 m
NTP4=−147677.761+104.799=−147572.962 m
ETP4=−29020.726+7.458=−29013.268 m
H2 (Kukagua):
Bearing: 303∘23′50.48′′=303.397356∘
Umbali: 99.362 m
ΔN=99.362cos(303.397356∘)=54.719 m
ΔE=99.362sin(303.397356∘)=−82.896 m
NH2=−147572.962+54.719=−147518.243 m
EH2=−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: 328∘59′36.48′′
TP1 - TP2: 06∘21′10.48′′
TP2 - TP3: 40∘31′45.48′′
TP3 - TP4: $\boxed{04^\circ
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Huu ni utatuzi wa swali la upimaji wa ardhi linalohusisha njia ya "ray trace traverse" kati ya alama za zamani W6 na H2.
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.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI 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 Hatua ya 1: Badilisha "bearings" kuwa digrii za desimali na kokotoa mabadiliko ya Northing ( N) na Easting ( E) kwa kila mstari. Tunatumia fomula: N = D (Bearing) na E = D (Bearing). W6 - TP1: Bearing: 329^ 01' 09'' = 329.019167^ Umbali: 67.227 m N = 67.227 (329.019167^) = 57.627 m E = 67.227 (329.019167^) = -34.591 m TP1 - TP2: Bearing: 06^ 22' 43'' = 6.378611^ Umbali: 99.962 m N = 99.962 (6.378611^) = 99.344 m E = 99.962 (6.378611^) = 11.095 m TP2 - TP3: Bearing: 40^ 33' 18'' = 40.555000^ Umbali: 101.759 m N = 101.759 (40.555000^) = 77.325 m E = 101.759 (40.555000^) = 66.137 m TP3 - TP4: Bearing: 04^ 05' 35'' = 4.093056^ Umbali: 105.032 m N = 105.032 (4.093056^) = 104.766 m E = 105.032 (4.093056^) = 7.497 m TP4 - H2: Bearing: 303^ 25' 23'' = 303.423056^ Umbali: 99.331 m N = 99.331 (303.423056^) = 54.713 m E = 99.331 (303.423056^) = -82.890 m Hatua ya 2: Jumlisha N na E zilizopimwa (kutoka W6 hadi H2). N_obs\_total = 57.627 + 99.344 + 77.325 + 104.766 + 54.713 = 393.775 m E_obs\_total = -34.591 + 11.095 + 66.137 + 7.497 - 82.890 = -32.732 m Hatua ya 3: Kokotoa N na 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 N_datum = N_H2 - N_W6 = -147518.260 - (-147912.146) = 393.886 m E_datum = E_H2 - E_W6 = -29096.233 - (-29063.323) = -32.910 m Hatua ya 4: Kokotoa Scale Factor (S) na Swing (). Tunatumia fomula: S = N_obs\_total N_datum + E_obs\_total E_datum N_obs\_total^2 + E_obs\_total^2 S = N_obs\_total E_datum - E_obs\_total N_datum N_obs\_total^2 + E_obs\_total^2 Kwanza, kokotoa denominator: N_obs\_total^2 + E_obs\_total^2 = (393.775)^2 + (-32.732)^2 = 155058.420625 + 1071.381924 = 156129.802549 Kisha, kokotoa nambari za S na S : N_obs\_total N_datum + E_obs\_total E_datum = (393.775)(393.886) + (-32.732)(-32.910) = 155099.07805 + 1077.20092 = 156176.27897 N_obs\_total E_datum - E_obs\_total N_datum = (393.775)(-32.910) - (-32.732)(393.886) = -12969.87525 - (-12899.78912) = -70.08613 Sasa, kokotoa S na S : S = (156176.27897)/(156129.802549) = 1.0003091 S = (-70.08613)/(156129.802549) = -0.0004489 Kutoka hapa, tunaweza kupata S na : S = sqrt((S )^2 + (S )^2) = sqrt((1.0003091)^2 + (-0.0004489)^2) = sqrt(1.0006182 + 0.0000002015) = sqrt(1.0006184015) = 1.0003091 = atan2(S , S ) = atan2(-0.0004489, 1.0003091) = -0.0004487 rad = -0.0257^ Badilisha kuwa digrii, dakika, sekunde: -0.0257^ = -0^ 01' 32.52'' Scale Factor: 1.0003091 Swing: -0^ 01' 32.52'' Sehemu (ii): Corrected Bearings na Distances na Final Coordinates Hatua ya 5: Rekebisha "bearings" kwa kuongeza "swing" angle. W6 - TP1: 329^ 01' 09'' - 0^ 01' 32.52'' = 328^ 59' 36.48'' TP1 - TP2: 06^ 22' 43'' - 0^ 01' 32.52'' = 06^ 21' 10.48'' TP2 - TP3: 40^ 33' 18'' - 0^ 01' 32.52'' = 40^ 31' 45.48'' TP3 - TP4: 04^ 05' 35'' - 0^ 01' 32.52'' = 04^ 04' 02.48'' TP4 - H2: 303^ 25' 23'' - 0^ 01' 32.52'' = 303^ 23' 50.48'' Hatua ya 6: Rekebisha umbali kwa kuzidisha na "scale factor". W6 - TP1: 67.227 × 1.0003091 = 67.248 m TP1 - TP2: 99.962 × 1.0003091 = 99.993 m TP2 - TP3: 101.759 × 1.0003091 = 101.790 m TP3 - TP4: 105.032 × 1.0003091 = 105.064 m TP4 - H2: 99.331 × 1.0003091 = 99.362 m Hatua ya 7: 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^ 59' 36.48'' = 328.993467^ Umbali: 67.248 m N = 67.248 (328.993467^) = 57.650 m E = 67.248 (328.993467^) = -34.610 m N_TP1 = -147912.146 + 57.650 = -147854.496 m E_TP1 = -29063.323 - 34.610 = -29097.933 m TP2: Bearing: 06^ 21' 10.48'' = 6.352911^ Umbali: 99.993 m N = 99.993 (6.352911^) = 99.366 m E = 99.993 (6.352911^) = 11.059 m N_TP2 = -147854.496 + 99.366 = -147755.130 m E_TP2 = -29097.933 + 11.059 = -29086.874 m TP3: Bearing: 40^ 31' 45.48'' = 40.529300^ Umbali: 101.790 m N = 101.790 (40.529300^) = 77.369 m E = 101.790 (40.529300^) = 66.148 m N_TP3 = -147755.130 + 77.369 = -147677.761 m E_TP3 = -29086.874 + 66.148 = -29020.726 m TP4: Bearing: 04^ 04' 02.48'' = 4.067356^ Umbali: 105.064 m N = 105.064 (4.067356^) = 104.799 m E = 105.064 (4.067356^) = 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^ 23' 50.48'' = 303.397356^ Umbali: 99.362 m N = 99.362 (303.397356^) = 54.719 m E = 99.362 (303.397356^) = -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: 328^ 59' 36.48'' TP1 - TP2: 06^ 21' 10.48'' TP2 - TP3: 40^ 31' 45.48'' TP3 - TP4: $04^ ✂️ _That answer was long and got cut off. Reply continue and I'll finish it._
