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Measurement, STD2 EQ-Bank 04 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 03

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

\(\text{Angular distance}\) \(=60+140=200^{\circ}\)
\(\therefore\ \text{Time Difference}\) \(=\dfrac{200}{15}\)
  \(=13.\dot{3}\)
  \(=13\ \text{hours}\ 20\ \text{minutes}\)

  
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` 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 SM-Bank 3

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
i.   `text(Angular difference in longitude)`

`= 113 – 38`

`= 75^@`
 

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

 

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

 

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

 
`text(Kenya is further East)`

COMMENT: NESA Nov-19 syllabus updates … use longitude to calculate time differences (1° = 4 mins).

`=>\ 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(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`