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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)
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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. \( (30^{\circ}\text{N}, 8^{\circ}\text{E}) \)
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\(D\)

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. \( (12^{\circ}\text{N}, 107^{\circ}\text{E}) \)
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\(C\)

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. \( 98^{\circ}\text{N} \), \( 135^{\circ}\text{W} \)
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\(B\)

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. \( 18^{\circ}\text{N} \), \( 169^{\circ}\text{W} \)
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\(D\)

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 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 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 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)

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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`