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Calcular analíticamente la longitud de llegada tras navegar 300 millas al rumbo verdadero 154º, si partimos de latitud 36° 50'2 N y longitud 123° 13'0 E.Compute analytically the arrival longitude after sailing 300 miles on true course 154º from latitude 36º 50.2' N, longitude 123º 13.0' E:
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Correct answer: a) L = 125º 52.7' E.
Why it is correct
With d = 300′ and Rv = 154º (S 26º E): ΔLat = 300 × cos 154º = −269.6′ = −4º 29.6′, giving Lat₂ = 32º 20.6′ N and mean latitude 34º 35.4′ N. Departure is A = 300 × sin 154º = 131.51′ E and ΔLong = 131.51 / cos 34º 35.4′ = 159.75′ E = +2º 39.7′ E ⇒ Long₂ = 123º 13.0′ E + 2º 39.7′ E = 125º 52.7′ E.
Why the others are not
- b) Does not properly apply ΔLong = departure / cos(mean Lat) added eastward from 123º 13.0′ E.
- c) Does not properly apply ΔLong = departure / cos(mean Lat) added eastward from 123º 13.0′ E.
- d) Does not properly apply ΔLong = departure / cos(mean Lat) added eastward from 123º 13.0′ E.
How to work it out in the exam
- Find ΔLat = d · cos 154º = −269.6′ to get arrival latitude (32º 20.6′ N) and mean latitude (34º 35.4′ N).
- Compute departure A = d · sin 154º = 131.5′ E, ΔLong = A / cos(mean Lat) = +2º 39.7′ E and add it to 123º 13.0′ E.
Where this question comes from
- Ministerio de Transportes (Madrid) · 2021 · Convocatoria de julio · PY Test 1 · question 40 Official paper · Official answer key
- Ministerio de Transportes (Madrid) · 2021 · Convocatoria de julio · PY Test 2 · question 37 Official paper · Official answer key
Try it: Navigation calculations
Pending instructor review. Machine translation, not reviewed.