Maths Quest A Year 11 for Queensland WorkSHEET 6.2 Chapter 6 Earth geometry Earth geometry WorkSHEET 6.2 1 Name: ___________________________ Use the world map above for the following questions, where necessary. 1 2 State whether the following pairs of points lie on the same line of longitude or the same line of latitude. (a) X (20ºN, 50ºE) and Y (20ºN, 50ºW) (a) latitude (b) P (50ºN, 50ºW) and Q (20ºN, 50ºW) (c) latitude (c) R (0º, 20ºE) and T (0º, 20ºW) (d) longitude (d) C (0º, 0º) and D (50ºS, 0º) (b) longitude Determine the angular distance between the following pairs of points. (a) A (23ºN, 0º) and B (50ºN, 0º) (a) angular distance = 50º – 23º = 27º (b) F (50ºS, 23ºW) and G (20ºN, 23ºW) (b) angular distance = 50º + 20º = 70º (c) J (70ºS, 50ºE) and K (70ºS, 40ºE) (d) X (0º, 20ºW) and Y (0º, 40ºE) (c) angular distance = 50º – 40º = 10º (d) angular distance = 20º + 40º = 60º Maths Quest A Year 11 for Queensland 3 Chapter 6 Earth geometry On a great circle, 1º 111.2 km. Calculate the distance in km between the following pairs of locations. (a) P (50ºS, 100ºE) and Q (12ºN, 100ºE) (b) A (40ºN, 20ºW) and B (75ºN, 20ºW) (c) C (0º, 40ºW) and D (0º, 20ºE) WorkSHEET 6.2 (a) angular distance distance in km (b) angular distance distance in km (c) angular distance distance in km 4 On a small circle, 1 111.2 km. cos km 5 P (40ºS, 20ºW) and Q (40ºS, 30ºE) When the angular distance between two locations is greater than 180º, the shortest distance between the two points is found by subtracting the angle from 360º. = 75º – 40º = 35º = 35 111.2 km = 3892 km = 40º + 20º = 60º = 60 111.2 km = 6672 km angular distance = 20º + 30º = 50º distance in km = 50 111.2 km cos 40º = 4259 km (a) These two points be on the same small circle (30ºN). Angular distance = 150º + 100º = 250º This is over 180º. So, shortest angular distance = 360º – 250º = 110º So, shortest distance between Y and Z = 110 111.2 cos 30º = 10 593 km (b) Points D and F lie on the same great circle (the equator) Angular distance = 110º + 120º = 230º This is over 180º. So, shortest angular distance = 360º – 230º = 130º So, shortest distance between D and F = 130 111.2 km = 14 456 km Find the shortest distance between the following pairs of points. (a) Y (30ºN, 150ºE) and Z (30ºN, 100ºW) (b) = 50º + 12º = 62º = 62 111.2 km = 6894.4 km (a) angular distance = 77º – 50º = 27º distance in km = 27 111.2 km cos 25º = 2721 km where parallel of latitude. Calculate the distance in km between the following pairs of locations (to the nearest km). (b) (a) X (25ºN, 50ºE) and Y (25ºN, 77ºE) (b) 2 D (0º, 110ºW) and F (0º, 120ºE) Maths Quest A Year 11 for Queensland 6 Chapter 6 Earth geometry The circumference of the equator represents an angular distance of 360º. This distance also represents a time period of 24 hours. Use this information to determine the time period equivalent to an angular distance of 1º of longitude. WorkSHEET 6.2 360 24 hours 24 1 hour 360 1 1 hour 15 1 1 60 min 15 1 4 min 7 8 9 (a) Longitude difference = 75º – 0º = 75º Time difference = 75 4 min = 300 min = 5 hours (b) Longitude difference = 75º + 150º = 225º Time difference = 225 4 min = 900 min = 15 hours Time zones throughout the world are quoted with reference to Greenwich Mean Time. Explain each of the following. (a) Brisbane time is 10 hours ahead of Greenwich Mean Time. (a) Brisbane is GMT + 10 (b) (b) New York is GMT – 5 New York time is 5 hours behind Greenwich Mean Time. Based on your answer for question 6, find the time difference between the following pairs of cities. (a) New York (40ºN, 75ºW) and London (51ºN, 0ºW) (b) New York (40ºN, 75ºW) and Sydney (34ºS, 150ºE) Find the time difference between the following (a) pairs of cities. (a) Los Angeles GMT – 8 and Brisbane GMT + 10 (b) Cape Town GMT + 1 and Brisbane GMT + 10 (b) Los Angles is 8 hours behind GMT and Brisbane is 10 hours ahead of GMT. Time difference 10 (8) 18 hours Cape Town is 1 hour ahead of GMT and Brisbane is 10 hours ahead of GMT. Time difference 10 (1) 9 hours 3 Maths Quest A Year 11 for Queensland 10 Chapter 6 Earth geometry Brisbane time is GMT +10. A plane leaves Brisbane on a flight to London (GMT) at 8 a.m. on Sunday. If the flight takes 20 hours, what will be the local time in London when it touches down? WorkSHEET 6.2 Departure time 8 a.m. Sunday Brisbane time Flight tim e 20 hours Arrival time 8 a.m. 20 hours (Brisbane time) 4 a.m. Monday (Brisbane time) Brisbane time is 10 hours ahead of London tim e Local time in London 4 a.m. Monday 10 hours 6 p.m. Sunday 4