A plane flies due west from point A (x°N, 15°E) to point B (x°N, 75°W). If the distance between A and B is 5005 km, calculate the position of point B. [R=6370 km, π=22/7]

Fresh day Oliverkoome@gmail254.Com., let's solve. 15. a) Calculate: i) position of point B. Point A is (x^N, 15^E). Point B is (x^N, 75^W). The aircraft flew due West, so the latitude x^ remains constant. The difference in longitude, , is the sum of the longitudes since one is East and the other is West. = 15^ + 75^ = 90^ The distance AB is given as 5005 km. The formula for distance along a parallel of latitude is D = ()/(360^) × 2 R x^. Given R = 6370 km and = (22)/(7). 5005 = (90)/(360) × 2 × (22)/(7) × 6370 × x^ 5005 = (1)/(4) × 2 × (22)/(7) × 6370 × x^ 5005 = (1)/(2) × (22)/(7) × 6370 × x^ 5005 = (11)/(7) × 6370 × x^ 5005 = 11 × 910 × x^ 5005 = 10010 × x^ x^ = (5005)/(10010) x^ = (1)/(2) x^ = ^-1((1)/(2)) x^ = 60^ So, the latitude of point B is 60^N. The position of point B is: 60^, 75^ ii) position of point C. From point B (60^N, 75^W), the aircraft flew due south. This means the longitude remains 75^W. The aircraft flew for 3 hours 40 minutes at an average speed of 910 km/h. Time taken for journey B to C = 3 hours 40 minutes = 3 + (40)/(60) hours = 3 + (2)/(3) hours = (11)/(3) hours. Distance BC = Speed × Time Distance BC = 910 km/h × (11)/(3) h = (10010)/(3) km The distance due south is along a meridian (a great circle). The formula for distance along a great circle is D = ()/(360^) × 2 R, where is the difference in latitude. (10010)/(3) = ()/(360) × 2 × (22)/(7) × 6370 (10010)/(3) = ()/(360) × 44 × 910 (10010)/(3) = ()/(360) × 40040 = (10010)/(3) × (360)/(40040) = (10010)/(3) × (360)/(4 × 10010) = (1)/(3) × (360)/(4) = (1)/(3) × 90^ = 30^ The difference in latitude is 30^. Since the aircraft flew south from 60^N, the new latitude is 60^ - 30^ = 30^N. The position of point C is: 30^, 75^ b) Determine the local time at point C when the aircraft arrived. Step 1: Calculate the time taken for the journey from A to B. Distance AB = 5005 km. Speed = 910 km/h. Time AB = Distance ABSpeed = 5005 km910 km/h = 5.5 hours = 5 hours 30 minutes Step 2: Calculate the local time at B when the aircraft arrived. Departure time from A (local time at A) = 0720h. Longitude of A = 15^E. Longitude of B = 75^W. Difference in longitude = 15^ + 75^ = 90^. Time difference due to longitude = (90^)/(15^/hour) = 6 hours. Since B is West of A, the local time at B is 6 hours earlier than the local time at A. Time at A when aircraft arrived at B = 0720h + 5h 30min = 1250h (local time at A). Local time at B when aircraft arrived = 1250h - 6h = 0650h. Step 3: Calculate the departure time from B. Stopover at B = 1 hour 30 minutes. Departure time from B (local time at B) = 0650h + 1h 30min = 0820h. Step 4: Calculate the arrival time at C. Time taken for journey B to C = 3 hours 40 minutes. Points B and C are on the same longitude (75^W), so their local times are the same. Arrival time at C (local time at C) = Departure time from B (local time at B) + Time taken for journey B to C. Arrival time at C = 0820h + 3h 40min = 1200h The local time at point C when the aircraft arrived is: 1200h Send me the next one 📸