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Measurement, STD2 EQ-Bank 23

Bangkok is located at \( (14^{\circ}\text{N}, 100^{\circ}\text{E}) \) and Montreal is located at \( (46^{\circ}\text{N}, 74^{\circ}\text{W}) \).

  1. Identify which city is closer to the Equator, giving reasons.   (1 mark)
  2. What is the difference in latitude between Bangkok and Montreal?   (1 mark)
  3. What is the difference in longitude between Bangkok and Montreal?   (1 mark)
Show Answers Only

a.   \(\text{Bangkok}\)

b.   \(32^{\circ}\)

c.   \(174^{\circ}\)

Show Worked Solution

a.   \(\text{Bangkok is at latitude }14^{\circ}\text{N} \)

\(\text{Montreal is at latitude }46^{\circ}\text{N} \)

\(\text{Since 14° < 46°, Bangkok is closer to the Equator.}\)
 

b.    \(\text{Latitude of Bangkok}=14^{\circ}\text{N}\)

\(\text{Latitude of Montreal}=46^{\circ}\text{N}\)

\(\text{Since cities are both in the northern hemisphere, subtract the latitudes.}\)

\(\text{Difference in latitude}=46^{\circ}-14^{\circ}=32^{\circ} \)
 

c.    \(\text{Longitude of Bangkok}=100^{\circ}\text{E}\)

\(\text{Longitude of Montreal}=74^{\circ}\text{W}\)

\(\text{Since cities on opposite sides of the Prime Meridian, add the longitudes.}\)

\(\text{Difference in longitude}=100^{\circ}+74^{\circ}=174^{\circ} \)

Measurement, STD2 EQ-Bank 22

Tokyo is located at \( (36^{\circ}\text{N}, 140^{\circ}\text{E}) \) and Lima is located at \( (12^{\circ}\text{S}, 77^{\circ}\text{W}) \).

  1. Explain which city is closer to the Prime Meridian?   (1 mark)
  2. What is the difference in latitude between Tokyo and Lima?   (1 mark)
  3. What is the difference in longitude between Tokyo and Lima?   (1 mark)
Show Answers Only

a.   \(\text{Lima}\)

b.   \(48^{\circ}\)

c.   \(217^{\circ}\)

Show Worked Solution

a.   \(\text{Tokyo is at longitude }140^{\circ}\text{E} \)

\(\text{Lima is at longitude }77^{\circ}\text{W} \)

\(\text{Since 77° < 140°, Lima is closer to the Prime Meridian.}\)
 

b.    \(\text{Latitude of Tokyo}=36^{\circ}\text{N}\)

\(\text{Latitude of Lima}=12^{\circ}\text{S}\)

\(\text{Since cities on opposite sides of the equator, add the latitudes.}\)

\(\text{Difference in latitude}=36^{\circ}+12^{\circ}=48^{\circ} \)
 

c.    \(\text{Longitude of Tokyo}=140^{\circ}\text{E}\)

\(\text{Longitude of Lima}=77^{\circ}\text{W}\)

\(\text{Since cities on opposite sides of the Prime Meridian, add the longitudes.}\)

\(\text{Difference in longitude}=140^{\circ}+77^{\circ}=217^{\circ} \)

Measurement, STD2 EQ-Bank 7 MC

The coordinates of Cairo are \( (30^{\circ}\text{N}, 31^{\circ}\text{E}) \).

What are the coordinates of Athens if it is 23° west of Cairo and on the same line of longitude?

  1. \( (30^{\circ}\text{N}, 54^{\circ}\text{E}) \)
  2. \( (7^{\circ}\text{N}, 31^{\circ}\text{E}) \)
  3. \( (53^{\circ}\text{N}, 31^{\circ}\text{E}) \)
  4. \( (30^{\circ}\text{N}, 8^{\circ}\text{E}) \)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Athens is 23° west of Cairo.}\)

\(\text{Latitude of Athens}=30^{\circ}\text{N}\)

\(\text{Longitude of Athens}=31^{\circ}-23^{\circ}=8^{\circ}\text{E}\)

\(\therefore\ \text{Coordinates of Athens are:}\ (30^{\circ}\text{N}, 8^{\circ}\text{E})\)

\(\Rightarrow D\)

Measurement, STD2 EQ-Bank 5 MC

The coordinates of Jakarta are \( (6^{\circ}\text{S}, 107^{\circ}\text{E}) \).

Darwin and Jakarta share the same longitude but Darwin is \( 18^{\circ} \) south of Jakarta. What are the coordinates of Darwin?

  1. \( (6^{\circ}\text{S}, 125^{\circ}\text{E}) \)
  2. \( (6^{\circ}\text{S}, 89^{\circ}\text{E}) \)
  3. \( (24^{\circ}\text{S}, 107^{\circ}\text{E}) \)
  4. \( (12^{\circ}\text{N}, 107^{\circ}\text{E}) \)
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Darwin is }18^{\circ}\text{ south of Jakarta.}\)

\(\text{Latitude of Darwin}=6^{\circ}+18^{\circ}=24^{\circ}\text{S}\)

\(\text{Longitude of Darwin}=107^{\circ}\text{E}\)

\(\therefore\ \text{Coordinates of Darwin are:}\ (24^{\circ}\text{S}, 107^{\circ}\text{E})\)

\(\Rightarrow C\)

Measurement, STD2 EQ-Bank 8 MC

City P is at latitude \( 42^{\circ}\text{N} \) and longitude \( 88^{\circ}\text{W} \). City Q is \( 56^{\circ} \) south of City P and \( 47^{\circ} \) west of City P.

What are the latitude and longitude of City Q?

  1. \( 14^{\circ}\text{N} \), \( 41^{\circ}\text{W} \)
  2. \( 14^{\circ}\text{S} \), \( 135^{\circ}\text{W} \)
  3. \( 14^{\circ}\text{S} \), \( 41^{\circ}\text{W} \)
  4. \( 98^{\circ}\text{N} \), \( 135^{\circ}\text{W} \)
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Latitude of City Q}=56^{\circ}-42^{\circ}=14^{\circ}\text{S}\)

\(\text{Longitude of City Q}=88^{\circ}+47^{\circ}=135^{\circ}\text{W}\)

\(\Rightarrow B\)

Measurement, STD2 EQ-Bank 13 MC

City A is at latitude \( 27^{\circ}\text{S} \) and longitude \( 153^{\circ}\text{E} \). City B is \( 45^{\circ} \) north of City A and \( 38^{\circ} \) east of City A.

What are the latitude and longitude of City B?

  1. \( 18^{\circ}\text{N} \), \( 191^{\circ}\text{E} \)
  2. \( 18^{\circ}\text{N} \), \( 115^{\circ}\text{E} \)
  3. \( 72^{\circ}\text{S} \), \( 191^{\circ}\text{E} \)
  4. \( 18^{\circ}\text{N} \), \( 169^{\circ}\text{W} \)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Latitude of City B}=45^{\circ}-27^{\circ}=18^{\circ}\text{N}\)

\(\text{Longitude of City B}=153^{\circ}+38^{\circ}=191^{\circ}\text{E}\)

\(\text{Since longitude}\ \gt 180^{\circ},\ \text{convert to Western hemisphere:\)

\(191^{\circ}-180^{\circ}=11^{\circ}\)

\(\text{Longitude}\ = 180-11=169^{\circ}\text{W}\)

\(\Rightarrow D\)

Measurement, STD2 EQ-Bank 15 MC

Singapore is located at longitude \(104^{\circ}\text{E}\) and Buenos Aires is located at longitude \(58^{\circ}\text{W}\). What is the time in Buenos Aires when it is 9:20 am in Singapore?

  1. 10:08 pm
  2. 8:32 pm
  3. 10:32 pm
  4. 8:08 am
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Longitudinal difference} = 104^{\circ}+58^{\circ}=162^{\circ}\)

\(\text{Calculate the time difference (using 15° = 1 hour time difference):}\)

\(\text{Time Difference} = \dfrac{162}{15} \text{ hours} = 10.8\text{ hours}=10\text{ hours}\ 48\ \text{minutes} \)

\(\text{Singapore is east of Buenos Aires}\ \ \Rightarrow\ \ \text{Singapore is ahead}\)

\(\text{Time in Singapore}\ =\ 9:20\ \text{am}\)

\(\therefore\ \text{Time in Buenos Aires}\) \(=9:20\ \text{am}-10\ \text{hours}\ 48\text{ minutes}\)
  \(=11:20\ \text{pm}-48\ \text{minutes}\)
  \(=10:32\ \text{pm (previous day)}\)

\(\Rightarrow C\)

Measurement, STD2 EQ-Bank 14 MC

London is located at longitude \(0^{\circ}\) (on the Prime Meridian) and Los Angeles is located at longitude \(118^{\circ}\text{W}\). What is the time in Los Angeles when it is 11:00 pm in London?

  1. 3:08 pm
  2. 6:52 pm
  3. 3:52 am
  4. 6:52 am
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Longitudinal difference}= 118^{\circ}-0=118^{\circ}\)

\(\text{Calculate time difference (using 15° = 1 hour):}\)

\(\text{Time Difference} = \dfrac{118}{15} \text{ hours} = 7.866\text{ hours}=7\text{ hours}\ 52\ \text{minutes} \)
 

\(\text{Los Angeles is west of London}\ \ \Rightarrow\ \ \text{Los Angeles is behind}\)

\(\text{Time in London}\ =\ 11:00\ \text{pm}\)

\(\therefore\ \text{Time in Los Angeles}\) \( = 11:00\ \text{pm}-7\ \text{hours}\ 52\text{ minutes}\)
  \(=\ 4:00\ \text{pm}-52\ \text{minutes}\)
  \(=3:08\ \text{pm}\)

\(\Rightarrow A\)

Measurement, STD2 EQ-Bank 4 MC

Melbourne is located at longitude \(145 ^{\circ}\text{E}\) and Tokyo is located at longitude \(140^{\circ}\text{E}\). Based purely on longitudinal difference, what is the time in Tokyo when it is 2:00 pm in Melbourne?

  1. 1:40 pm
  2. 1:48 pm
  3. 2:12 pm
  4. 2:20 pm
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Longitudinal difference} = 145^{\circ}-140^{\circ} = 5^{\circ} \)

\(\text{Time difference (15° = 1 hour time difference):}\)

\(\text{Time Difference} = \dfrac{5}{15} \text{ hours} = \dfrac{1}{3} \text{ hour} = 20 \text{ minutes} \)
 

\(\text{Since Melbourne is further east}\ \ \Rightarrow\ \ \text{it is ahead}\)

\(\text{Time in Melbourne}\ =\ 2:00\ \text{pm}\)

\(\text{Time in Tokyo}= 2:00\ \text{pm}-20\ \text{minutes}=\ 1:40\ \text{pm}\)

\(\Rightarrow A\)

Measurement, STD2 EQ-Bank 12 MC

Tokyo is 45\(^{\circ}\) west of Sydney. Using longitudinal difference, what is the time in Tokyo when it is 3:00 pm in Sydney?

  1. 6:00 am
  2. 9:00 am
  3. 6:00 pm
  4. 12:00 pm
Show Answers Only

\(D\)

Show Worked Solution

\(15^{\circ}\ =\text{1 hour time difference}\)

\(\text{Longitudinal distance}=45^{\circ}\)

\(\text{Time Difference}=\dfrac{45}{15}=3\ \text{hours}\)

  
\(\text{Time in Sydney}\ =\ 3:00\ \text{pm}\)

\(\text{Since Sydney is East of Tokyo:}\)

\(\text{Time in Tokyo}=\ 3:00\ \text{pm}-3\ \text{hours}=\ 12:00\ \text{pm}\)

\(\Rightarrow D\)

Measurement, STD2 EQ-Bank 4 MC

Kathmandu is  30\(^{\circ}\) west of Perth. Using longitudinal distance, what is the time in Kathmandu when it is noon in Perth?

  1. 10:00 am
  2. 11:30 am
  3. 12:30 pm
  4. 2:00 pm
Show Answers Only

\(A\)

Show Worked Solution

\(15^{\circ}\ =\text{1 hour time difference}\)

\(\text{Longitudinal distance}\) \(=30^{\circ}\)
\(\therefore\ \text{Time Difference}\) \(=\dfrac{30}{15}\)
  \(=2\ \text{hours}\)

  
\(\text{Time in Perth}\ =\ 12\ \text{pm}\)

\(\therefore\ \text{Time in Kathmandu}\) \( =\ 12\ \text{pm}\ -\ 2\ \text{hours}\)
  \(=\ 10:00\ \text{am}\)

\(\Rightarrow A\)

Measurement, STD2 EQ-Bank 25

The table shows the approximate coordinates of two cities.

\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{City} \rule[-1ex]{0pt}{0pt} & \textit{Latitude} \rule[-1ex]{0pt}{0pt} & \textit{Longitude}\\
\hline
\rule{0pt}{2.5ex} \text{Buenos Aires} \rule[-1ex]{0pt}{0pt} & 35^{\circ}\ \text{S} \rule[-1ex]{0pt}{0pt} & 60^{\circ}\ \text{W}  \\
\hline
\rule{0pt}{2.5ex} \text{Adelaide} \rule[-1ex]{0pt}{0pt} & 35^{\circ}\ \text{S}  \rule[-1ex]{0pt}{0pt} & 140^{\circ}\ \text{E}  \\
\hline
\end{array}

  1. What is the time difference between Adelaide and Buenos Aires?   (2 marks)
  3. Roy lives in Adelaide and his cousin Juan lives in Buenos Aires. Roy wants to telephone Juan at 7 pm on Friday night, Buenos Aires time.
  4. At what time, and on what day, should Roy make the call?   (2 marks)
Show Answers Only

a.    \(13\ \text{hours}\ 20\ \text{minutes}\)

b.    \(8:20\ \text{am on Saturday}\)

Show Worked Solution

a.    \(15^{\circ}\ =\text{1 hour time difference}\)

\(\text{Angular distance}=60+140=200^{\circ}\)

\(\text{Time Difference}=\dfrac{200}{15}=13.\dot{3}=13\ \text{hours}\ 20\ \text{minutes}\)

  
b.    \(\text{Time in Buenos Aires}\ =\ 7\ \text{pm Friday night}\)

\(\therefore\ \text{Time in Adelaide}\) \( =\ 7\ \text{pm}\ +\ 13\ \text{hours}\ 20\ \text{minutes}\)
  \(=\ 8:20\ \text{am on Saturday}\)

Measurement, STD2 M2 2023 HSC 7 MC

City `A` is at latitude 34°S and longitude 151°E. City `B` is 72° north of City `A` and 25° west of City `A`.

What are the latitude and longitude of City `B`?

  1. 16°N, 126°E
  2. 16°N, 176°E
  3. 38°N, 126°E
  4. 38°N, 176°E
Show Answers Only

`C`

Show Worked Solution

`text{Latitude of city}\ A: \ -34+72=38°text{N}`

`text{Longitude of city}\ A: \ 151-25=126°text{E}`

`=>C`

Measurement, STD2 M2 2021 HSC 20

City A is in Sweden and is located at (58°N, 16°E). Sydney, in Australia, is located at (33°S, 151°E).

Robert lives in Sydney and needs to give an online presentation to his colleagues in City A starting at 5:00 pm Thursday, local time in Sweden.

What time and day, in Sydney, should Robert start his presentation?

It is given that 15° = 1 hour time difference. Ignore daylight saving.  (3 marks)

Show Answers Only

`text(2 am Friday)`

Show Worked Solution

`text{Angular difference}\ = 151 – 16 = 135°`

Mean mark 52%.

`=>\ text{Time difference}\ = 135/15 = 9\ text(hours)`

`text(Sydney is east of Sweden → ahead)`
 

`text{Presentation time (Sydney)}` `=\ text(5 pm Thurs + 9 hours)`  
  `=\ text(2 am Friday)`  

Measurement, STD2 M2 2011 HSC 27b

Pontianak has a longitude of 109°E, and Jarvis Island has a longitude of 160°W.

Both places lie on the Equator. 

  1. Calculate the shortest distance between these two places (`d`), to the nearest kilometre, using

     

      `d=theta/360 xx  2pir`  where  `theta=91°`  and  `r=6400\ \text{km}`   (1 mark)

  2. The position of Rabaul is 4° to the south and 48° to the west of Jarvis Island. What is the latitude and longitude of Rabaul?    (2 marks)

Show Answers Only
  1. `10\ 165\ text(km)\ \ \ text{(nearest km)}`
  2. `(4^@text{S}, 152^@text{E})`
Show Worked Solution
a.  `text(Shortest distance)` `= 91/360 xx 2 pi r`
  `= 91/360 xx 2 xx pi xx 6400`
  `= 10\ 164.79…`
  `=10\ 165\ text(km)\ text{(nearest km)}`

 

♦♦ Mean mark (b) 33%

b.    `text(Latitude:)`

`4^@\ text(South of Jarvis Island)`

`text{Since Jarvis Island is on equator, Rabaul’s latitude is 4°S.}`
 

`text(Longitude:)`

`text(Jarvis Island is)\ 160^@ text(W)`

`text(Rubail is)\ 48^@\ text(West of Jarvis Island, or 208° West)`

`text(which is)\ 28^@\ text{past meridian (180°)}`

`text(Longitude)= (180-28)^@ text(E)= 152^@ text(E)`

`:.\ text(Rabaul’s position is)\ (4^@text{S}, 152^@text{E})`

Measurement, STD2 M2 SM-Bank 28

An aircraft travels at an average speed of  913 km/h. It departs from a town in Kenya  (0°, 38°E)  on Tuesday at 10 pm and flies east to a town in Borneo  (0°, 113°E).

  1. Calculate the distance (`d`), to the nearest kilometre, between the two towns, using

     

    `d=theta/360 xx 2 pi r`  where  `theta = 75^@`  and  `r=6400` km  (2 marks)

  2. How long will the flight take? (Answer to the nearest hour.)   (1 mark)

  3. What will be the day and local time in Borneo when the aircraft arrives? (Ignore time zones.)   (2 marks)

Show Answers Only
  1. `8378\ text(km)`
  2. `9\ text(hours)`
  3. `text(12 midday on Wednesday)`
Show Worked Solution

a.    `\text{Longitudinal difference}=113-38= 75^@` 

`text(Distance)` `= 75/360 xx 2 xx pi xx 6400`
  `= 8377.58…`
  `= 8378\ text(km)\ text{(nearest km)}`

 

b.    `text(Flight time)` `= text(Distance)/text(Speed)`
    `= 8378/913`
    `= 9.176…`
    `= 9\ text(hours)\ text{(nearest hr)}`

 
c.    `text(Time Difference)= 75 xx 4= 300\ text(minutes)= 5\ text(hours)`

`text(Kenya is further East)\ =>\ text(Kenya is +5 hours)`

`:.\ text(Arrival time in Kenya)`

`= text{10 pm (Tues) + 5 hrs + 9 hrs}\ text{(flight)}`

`= 12\ text(midday on Wednesday)`

Measurement, STD2 M2 2017 HSC 27d

Island A and island B are both on the equator. Island B is west of island A. The longitude of island A is 5°E and the angle at the centre of Earth (O), between A and B, is 30°.
 

  1. What is the latitude and longitude of island `B`?  (2 marks)

  2. What time is it on island `B` when it is 10 am on island `A`?  (1 mark)

Show Answers Only

a.   `(0°, 25W)`

b.   `8\ text(am)`

Show Worked Solution

a.    `text{Longitude (island}\ B)= 5-30= -25= 25^@\ text(W)`

`text{Latitude (island}\ B)=0^@`

`:.\ text(Island)\ B\ text{is  (0°, 25°W).}`
 

b.    `text(Time difference) = 30 xx 4 = 120 \ text(mins)\ =2\ text(hours)`

`text(S)text(ince)\ B\ text(is west of)\ A:`

`text(Time on island)\ B= 10\ text(am less 2 hours)= 8\ text(am)`

♦ Mean marks (a) 40% and (b) 45%.

Measurement, STD2 M2 2010 HSC 15 MC

In this diagram of the Earth, `O` represents the centre and `B` lies on both the Equator and the Greenwich Meridan.
 

What is the latitude and longitude of point `A`?

  1.    `\text{30°N  110°E}`
  2.   `\text{30°N  110°W}`
  3.   `\text{60°N  110°E}`
  4.   `\text{60°N  110°W}`
Show Answers Only

`A`

Show Worked Solution

 `text{Since}\ A\ \text{is 30° North of the Equator}`

   `=> text{Latitude}\ =30^circ \text{N}`

  `text{Since}\ A\ \text{is 110° East of Greenwich}`

   `=>text{Longitude}\ =110^circ \text{E}`
 

`:. \ \text{Coordinates of}\ A\ \text{= (30°N, 110°E)}`

`=>  A`