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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^(circ)text{N}`

`text{Longitude of city}\ A: \ 151-25=126^(circ)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

a.   `10\ 165\ text(km)\ \ \ text{(nearest km)}`

b.   `(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`