Problem C – two possible solutions Solution 2 Solution 1 The typical flight time from UK to New York, following a small circle across the The width of the north Atlantic ocean: North Atlantic, is about 6 hours. Modern aircraft fly about 1,000 km/hr. On a world map this accounts for about ¼ of the circumference of the Earth at about the latitude of the UK. distance = speed × time = 1,000 km/hr × 6 hr Earth’s radius is 6,400 km; the southern UK is about 45º north. = 6,000 km º) The radius of the small circle at 45º N = sin(45 ≈ 0.7 of that at the equator. Time for north Atlantic to open = distance / speed The radius of the Earth at the equator ≈ 6,400 km. = 6,000 km / (2.5 x 10-5) km/year So the radius of the small circle at 45º N ≈ 0.7 × 6,400 km = 2.4 x 108 year = 4,500 km = 240 Myr Width of the north Atlantic at 45º N = ¼ × (2 π) × 4,500 km = π/2 × 4,500 km Comment: ≈ 7,000 km. Both answers seem reasonable. Time for north Atlantic to open = distance / speed = 7,000 km / (2.5 x 10-5) km/year However, the main phase of central/north Atlantic opening coincides with the = 2.5 x 108 year eruption of the Central Atlantic Magmatic Province (CAMP), which is very well = 280 Myr exposed in both New England (USA) and Morocco. This event is dated at about 200 Ma, so the long term average rate of plate motion must be closer to 3 cm/yr. Key Stage 5 - Volcano Back of the envelope
Problem C – two possible solutions Solution 1 The width of the north Atlantic ocean: On a world map this accounts for about ¼ of the circumference of the Earth at about the latitude of the UK. Earth’s radius is 6,400 km; the southern UK is about 45º north. The radius of the small circle at 45º N = sin(45 º) ≈ 0.7 of that at the equator. The radius of the Earth at the equator ≈ 6,400 km. So the radius of the small circle at 45º N ≈ 0.7 × 6,400 km = 4,500 km Width of the north Atlantic at 45º N = ¼ × (2 π) × 4,500 km = π/2 × 4,500 km ≈ 7,000 km. Time for north Atlantic to open = distance / speed = 7,000 km / (2.5 x 10-5) km/year = 2.5 x 108 year = 280 Myr Solution 2 The typical flight time from UK to New York, following a small circle across the North Atlantic, is about 6 hours. Modern aircraft fly about 1,000 km/hr. distance = speed × time = 1,000 km/hr × 6 hr = 6,000 km Time for north Atlantic to open = distance / speed = 6,000 km / (2.5 x 10-5) km/year = 2.4 x 108 year = 240 Myr Comment: Both answers seem reasonable. However, the main phase of central/north Atlantic opening coincides with the eruption of the Central Atlantic Magmatic Province (CAMP), which is very well exposed in both New England (USA) and Morocco. This event is dated at about 200 Ma, so the long term average rate of plate motion must be closer to 3 cm/yr. Key Stage 5 - Volcano Back of the envelope