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Calcular analiticamente el rumbo y la distancia que ha de recorrer una embarcacion para ir desde la situacion inicial de coordenadas: l=36º46´ N, L=010º30´ W, hasta una situacion final de coordenadas: l=33º 40´N, L=008º 35´W.Compute analytically the rhumb-line course and distance from initial position 36º 46' N, 010º 30' W to final position 33º 40' N, 008º 35' W:
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Correct answer: b) R = 153º; d = 208.4'
Why it is correct
ΔLat = 33º 40′ N − 36º 46′ N = −186.0′ (S) and ΔLong = 008º 35′ W − 010º 30′ W = +115.0′ (E). With mean latitude 35º 13′ N, departure is A = 115.0′ × cos 35º 13′ = 93.95′ E; tan R = 93.95 / 186.0 ⇒ R = S 26.8º E ≈ 153º and d = √(186.0² + 93.95²) = 208.4 miles.
Why the others are not
- a) Does not result from applying the direct rhumb-line formulas with ΔLat = 186′ S and departure = 94.0′ E.
- c) Does not result from applying the direct rhumb-line formulas with ΔLat = 186′ S and departure = 94.0′ E.
- d) Does not result from applying the direct rhumb-line formulas with ΔLat = 186′ S and departure = 94.0′ E.
How to work it out in the exam
- Find ΔLat = 186.0′ S, ΔLong = 115.0′ E and mean latitude 35º 13′ N.
- Find departure A = ΔLong · cos(mean Lat) = 93.95′ E, course tan R = A / ΔLat (S 26.8º E = 153º) and distance d = ΔLat / cos R = 208.4′.
Where this question comes from
- Ministerio de Transportes (Madrid) · 2021 · Convocatoria de julio · PY Test 1 · question 36 Official paper · Official answer key
- Ministerio de Transportes (Madrid) · 2021 · Convocatoria de julio · PY Test 2 · question 35 Official paper · Official answer key
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Pending instructor review. Machine translation, not reviewed.