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GEOMETRY, FUR1 2021 VCAA 1 MC

Which one of the following cities is closest to the Greenwich meridian?

  1. Barcelona (41° N, 2° E)
  2. Berlin (53° N, 13° E)
  3. Edinburgh (56° N, 3° W)
  4. Lomé (6° N, 1° E)
  5. Nairobi (1° N, 37° E)
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`D`

Show Worked Solution

`text{Greenwich meridian has longitude} \ 0^@`

`text{Lome at} \ 1^@ \ text{is the closest.}`
 

`=> D`

GEOMETRY, FUR1 2017 VCAA 3 MC

The locations of four cities are given below.

Adelaide (35° S, 139° E)     Buenos Aires (35° S, 58° W) 
Melilla (35° N, 3° W)      Heraklion (35° N, 25° E)

 

In which order, from first to last, will the sun rise in these cities on New Year’s Day 2018?

  1. Adelaide, Heraklion, Buenos Aires, Melilla
  2. Adelaide, Heraklion, Melilla, Buenos Aires
  3. Heraklion, Adelaide, Melilla, Buenos Aires
  4. Melilla, Adelaide, Heraklion, Buenos Aires
  5. Melilla, Adelaide, Buenos Aires, Heraklion
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`B`

Show Worked Solution

`text(Sun rises in the East.)`

`text(Adelaide is further east than Heraklion.)`

`text(Melilla is further east (i.e. less west))`

`text(than Buenos Aires.)`

`:.\ text{Order is: Adelaide (139°E) , Heraklion (25°E),}`

    `text{Melilla (3°W), Buenos Aires (58°W)}`

`=> B`

GEOMETRY, FUR1 SM-Bank 11 MC

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

 2010 15 MC

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

A.   `text(30°N  110°E)`

B.   `text(70°N  30°W)`

C.   `text(110°N  60°E)`

D.   `text(30°N  110°W)`

E.    `text(60°N  110°W)`

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`A`

Show Worked Solution

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

   `→ text(Latitude is)  30^circ text(N)`

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

    `→ text(Longitude is)  110^circ text(E)`

`:. A\ text(coordinates are:) \  30^circ text(N)  110^circ text(E)`

`=>  A`

GEOMETRY, FUR2 SM-Bank 14

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

Both places lie on the Equator

  1. Find the shortest great circle distance between these two places, to the nearest kilometre. You may assume that the radius of the Earth is 6400 km.    (2 marks)
  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?     (1 mark)
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  1. `10\ 165\ text(km)\ \ \ text{(nearest km)}`
  2. `152^@ text(E)`
Show Worked Solution
a.   `text(Longitude difference)` `= 109 + 160`
    `= 269^@`

 

`=> text(Shortest distance)\ text{(by degree)}` `= 360 – 269`
  `= 91^@`

 

`:.\ 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)}`

 

b.   `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})`