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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°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` 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. `152^@ text(E)`
Show Worked Solution
i.  `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 33%
ii. `text(Latitude)`
  `4^@\ text(South of Jarvis Island)`
  `text(S)text(ince Jarvis Island is on equator)`
  `=> text(Latitude is)\ 4^@ text(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(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)

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(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.    30°N  110°E
  2.    30°N  110°W
  3.    60°N  110°E
  4.    60°N  110°W
Show Answers Only

`A`

Show Worked Solution

 `text(S)text(ince A is)  30^circ\  text(North of the Equator)`

   `=> text(Latitude is)  30^circN`

  `text(S)text(ince A is)  110^circ\  text(East of Greenwich)`

    `=>text(Longitude is)  110^circE`
 

`:. A\ text(is) \ \  30^circN  110^circE`

`=>  A`