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Solutions — Latitude and Longitude

  1. Fluency Coordinates of given points.
    (a) North Pole: (90°N, any longitude) — the North Pole has latitude 90°N but longitude is undefined (all meridians meet there).
    (b) On the equator at the prime meridian: (0°, 0°)
    (c) (45°S, 90°W) — this is how coordinates are written (lat, long).
  2. Fluency Which is further from the equator: 30°N or 55°S?
    30°N is 30° from the equator.
    55°S is 55° from the equator.
    55°S is further from the equator by 55 − 30 = 25 degrees.
  3. Fluency Longitude difference between 20°N, 30°E and 20°N, 80°E.
    Both are east of the prime meridian, so: 80° − 30° = 50°
    The cities are 50 degrees of longitude apart.
  4. Fluency Hemispheres for (42°S, 174°E).
    42°S → Southern Hemisphere
    174°E → Eastern Hemisphere
    (This is near Wellington, New Zealand.)
  5. Understanding Brisbane (27.5°S, 153°E) and Sydney (34°S, 151°E).
    Difference in latitude: 34° − 27.5° = 6.5°
    Brisbane is at 27.5°S and Sydney is at 34°S. Brisbane is closer to the equator (smaller latitude value means closer to equator).
  6. Understanding Two ships at (0°, 30°W) and (0°, 60°E).
    Angular separation: 30° + 60° = 90° (opposite sides of prime meridian, so add)

    Distance along equator:
    d = (2π × 6400 × 90) / 360 = (2π × 6400) / 4 = π × 3200 ≈ 10 053 km
  7. Understanding Plane flies from (10°S, 140°E) to (20°N, 140°E).
    Angular change in latitude: 10° + 20° = 30° (crosses equator, so add)

    Distance: d = (2π × 6400 × 30) / 360 = (2π × 6400) / 12 ≈ 3 351 km
  8. Understanding Cities on the same meridian / same parallel.
    Same meridian (longitude): Examples — London (0°) and Accra, Ghana (0°); or Brisbane (≈153°E) and Tokyo (≈140°E, not exact but close).

    Same parallel (latitude): Examples — Perth, WA (≈32°S) and Buenos Aires, Argentina (≈34°S, close); or Madrid, Spain (≈40°N) and New York (≈40°N).

    (Many valid answers exist — the key concept is that same longitude means on the same north-south line; same latitude means on the same east-west ring.)
  9. Problem Solving Points A (40°N, 20°W) and B (40°S, 20°W).
    (a) A and B are on opposite sides of the equator: angular difference = 40 + 40 = 80°

    (b) Distance along meridian:
    d = (2π × 6400 × 80) / 360 = (2π × 6400 × 2) / 9 ≈ (80 424 × 2) / 9 ≈ 8 936 km

    (c) Fraction of full circumference = 80/360 = 2/9 ≈ 22.2%
  10. Problem Solving Ship along Tropic of Capricorn from 115°E to 154°E.
    (a) Longitude change: 154° − 115° = 39°

    (b) Radius of the circle at 23.5°S:
    r = 6400 × cos(23.5°) = 6400 × 0.9171 ≈ 5869 km

    Distance = (2π × 5869 × 39) / 360 ≈ (36 875 × 39) / 360 ≈ 3 995 km ≈ 3 995 km

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