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Measurement, STD2 EQ-Bank 15 MC

Singapore is located at longitude \(104^{\circ}\text{E}\) and Buenos Aires is located at longitude \(58^{\circ}\text{W}\). What is the time in Buenos Aires when it is 9:20 am in Singapore?

  1. 10:08 pm
  2. 8:32 pm
  3. 10:32 pm
  4. 8:08 am
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\(C\)

Show Worked Solution

\(\text{Longitudinal difference} = 104^{\circ}+58^{\circ}=162^{\circ}\)

\(\text{Calculate the time difference (using 15° = 1 hour time difference):}\)

\(\text{Time Difference} = \dfrac{162}{15} \text{ hours} = 10.8\text{ hours}=10\text{ hours}\ 48\ \text{minutes} \)

\(\text{Singapore is east of Buenos Aires}\ \ \Rightarrow\ \ \text{Singapore is ahead}\)

\(\text{Time in Singapore}\ =\ 9:20\ \text{am}\)

\(\therefore\ \text{Time in Buenos Aires}\) \(=9:20\ \text{am}-10\ \text{hours}\ 48\text{ minutes}\)
  \(=11:20\ \text{pm}-48\ \text{minutes}\)
  \(=10:32\ \text{pm (previous day)}\)

\(\Rightarrow C\)

Measurement, STD2 EQ-Bank 14 MC

London is located at longitude \(0^{\circ}\) (on the Prime Meridian) and Los Angeles is located at longitude \(118^{\circ}\text{W}\). What is the time in Los Angeles when it is 11:00 pm in London?

  1. 3:08 pm
  2. 6:52 pm
  3. 3:52 am
  4. 6:52 am
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\(A\)

Show Worked Solution

\(\text{Longitudinal difference}= 118^{\circ}-0=118^{\circ}\)

\(\text{Calculate time difference (using 15° = 1 hour):}\)

\(\text{Time Difference} = \dfrac{118}{15} \text{ hours} = 7.866\text{ hours}=7\text{ hours}\ 52\ \text{minutes} \)
 

\(\text{Los Angeles is west of London}\ \ \Rightarrow\ \ \text{Los Angeles is behind}\)

\(\text{Time in London}\ =\ 11:00\ \text{pm}\)

\(\therefore\ \text{Time in Los Angeles}\) \( = 11:00\ \text{pm}-7\ \text{hours}\ 52\text{ minutes}\)
  \(=\ 4:00\ \text{pm}-52\ \text{minutes}\)
  \(=3:08\ \text{pm}\)

\(\Rightarrow A\)

Measurement, STD2 EQ-Bank 4 MC

Melbourne is located at longitude \(145 ^{\circ}\text{E}\) and Tokyo is located at longitude \(140^{\circ}\text{E}\). Based purely on longitudinal difference, what is the time in Tokyo when it is 2:00 pm in Melbourne?

  1. 1:40 pm
  2. 1:48 pm
  3. 2:12 pm
  4. 2:20 pm
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\(A\)

Show Worked Solution

\(\text{Longitudinal difference} = 145^{\circ}-140^{\circ} = 5^{\circ} \)

\(\text{Time difference (15° = 1 hour time difference):}\)

\(\text{Time Difference} = \dfrac{5}{15} \text{ hours} = \dfrac{1}{3} \text{ hour} = 20 \text{ minutes} \)
 

\(\text{Since Melbourne is further east}\ \ \Rightarrow\ \ \text{it is ahead}\)

\(\text{Time in Melbourne}\ =\ 2:00\ \text{pm}\)

\(\text{Time in Tokyo}= 2:00\ \text{pm}-20\ \text{minutes}=\ 1:40\ \text{pm}\)

\(\Rightarrow A\)

Measurement, STD2 EQ-Bank 12 MC

Tokyo is 45\(^{\circ}\) west of Sydney. Using longitudinal difference, what is the time in Tokyo when it is 3:00 pm in Sydney?

  1. 6:00 am
  2. 9:00 am
  3. 6:00 pm
  4. 12:00 pm
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\(D\)

Show Worked Solution

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

\(\text{Longitudinal distance}=45^{\circ}\)

\(\text{Time Difference}=\dfrac{45}{15}=3\ \text{hours}\)

  
\(\text{Time in Sydney}\ =\ 3:00\ \text{pm}\)

\(\text{Since Sydney is East of Tokyo:}\)

\(\text{Time in Tokyo}=\ 3:00\ \text{pm}-3\ \text{hours}=\ 12:00\ \text{pm}\)

\(\Rightarrow D\)

Measurement, STD2 EQ-Bank 4 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 25

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)
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a.    \(13\ \text{hours}\ 20\ \text{minutes}\)

b.    \(8:20\ \text{am on Saturday}\)

Show Worked Solution

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

\(\text{Angular distance}=60+140=200^{\circ}\)

\(\text{Time Difference}=\dfrac{200}{15}=13.\dot{3}=13\ \text{hours}\ 20\ \text{minutes}\)

  
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 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 SM-Bank 28

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

a.    `\text{Longitudinal difference}=113-38= 75^@` 

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

 

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

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

`text(Kenya is further East)\ =>\ 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{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%.