# Maths Quest a Year 11 for Queenslandchapter 6 Earth Geometry Worksheet 6.21

Maths Quest A Year 11 for QueenslandChapter 6 Earth geometry WorkSHEET 6.21

**WorkSHEET 6.2Earth geometry**Name: ______

Use the world map above for the following questions, where necessary.

1 / 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)

(b)P (50ºN, 50ºW) and Q (20ºN, 50ºW)

(c)R (0º, 20ºE) and T (0º, 20ºW)

(d)C (0º, 0º) and D (50ºS, 0º) / (a)latitude

(b)longitude

(c)latitude

(d)longitude

2 / Determine the angular distance between the following pairs of points.

(a)A (23ºN, 0º) and B (50ºN, 0º)

(b)F (50ºS, 23ºW) and G (20ºN, 23ºW)

(c)J (70ºS, 50ºE) and K (70ºS, 40ºE)

(d)X (0º, 20ºW) and Y (0º, 40ºE) / (a)angular distance= 50º – 23º

= 27º

(b)angular distance= 50º + 20º

= 70º

(c)angular distance= 50º – 40º

= 10º

(d)angular distance= 20º + 40º

= 60º

3 / On a great circle, 1º 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) / (a)angular distance= 50º + 12º

= 62º

distance in km= 62 111.2 km

= 6894.4 km

(b)angular distance= 75º – 40º

= 35º

distance in km= 35 111.2 km

= 3892 km

(c)angular distance= 40º + 20º

= 60º

distance in km= 60 111.2 km

= 6672 km

4 / On a small circle,

Calculate the distance in km between the following pairs of locations (to the nearest km).

(a)X (25ºN, 50ºE) and Y (25ºN, 77ºE)

(b)P (40ºS, 20ºW) and Q (40ºS, 30ºE) / (a)angular distance= 77º – 50º

= 27º

distance in km= 27 111.2 km cos 25º

= 2721 km

(b)angular distance= 20º + 30º

= 50º

distance in km= 50 111.2 km cos 40º

= 4259 km

5 / 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.

Find the shortest distance between the following pairs of points.

(a)Y (30ºN, 150ºE) and Z (30ºN, 100ºW)

(b)D (0º, 110ºW) and F (0º, 120ºE) / (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

6 / 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. /

7 / 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) / (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

8 / Time zones throughout the world are quoted with reference to Greenwich Mean Time. Explain each of the following.

(a)Brisbane is GMT + 10

(b)New York is GMT – 5 / (a)Brisbane time is 10 hours ahead of Greenwich Mean Time.

(b)New York time is 5 hours behind Greenwich Mean Time.

9 / Find the time difference between the following pairs of cities.

(a)Los Angeles GMT – 8 and

Brisbane GMT + 10

(b)Cape Town GMT + 1 and

Brisbane GMT + 10 / (a)Los Angles is 8 hours behind GMT and Brisbane is 10 hours ahead of GMT.

(b)Cape Town is 1 hour ahead of GMT and Brisbane is 10 hours ahead of GMT.

10 / 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? /