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Measurement, STD1 M2 2021 HSC 15

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 25%.

`=>\ 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 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)`