Help in Answering a geosystems question - please

[Bhowdy44]

" on her birthday, which happens to fall on september 21st, amelia is flying due east. as the sun rises and begins to bathe her elegant craft in golden light, the radio crackles and an announcer informs her- in a british accent, of course-that it is 2:00 pm greenwich time. hour after hour amelia maintains her course, cruising at an average speed of 105 miles per hour. all day long she sees nothing but water down below and when the sun sets she notes that only ten hours have elapsed since sunrise. along what line of latitude has amelia been traveling ? "

[ChuckFickens]

I can narrow it down to either 60° north, 20° north, 60° south, or 20° south.

[vascop]

Are we to assume from the date that day and night are both equal to 12 hours?
Chuck - presumably this must be the southern hemisphere as she can only see water below?
What do we take the radius of the earth to be? 4000 miles?

[mike11111]

From the question day is 10 hours and night is 14 hours at the time of the autumn equinox. The question is: on which degree of latitude would that happen in the Southern hemisphere. I'm afraid i don't know.

[R1Geezer]

the antarctic circle

[jake-the-peg]

The date is on the equinox when the day is as long as the night (12 hours) all over the planet.

For her however the day only lasts 10 hours because she is flying towards the approaching terminator (line between day and night)

In that 10 hours she has travelled 1,050 miles (I'm assuming that's statute rather than nautical miles)

Assuming the Earth to be spherical the distance around the circle at lattitude x is 2*pi*radius*cos(x) (radius of the Earth 3960 miles)

so the 1050 miles represents the distance the terminator travels in 2 hours or 2/24 * that value

so 2/24 *2* pi * 3960 * cos(x) =1050

0.506=cos(x)

x = 59.57 degrees North or South

[jake-the-peg]

On second thoughts Nort - doesn't look as if there is any land at 60 degrees south

http://en.wikipedia.o...i/60th_parallel_south

[jomifl]

Bear in mind she started at dawn 120 degrees west

[jomifl]

There is no land at latitude 60 dgrees south according to my atlas

[jake-the-peg]

That would make it in BC http://confluence.org...e.php?lat=60&lon=-120

A very long way from the sea

GMT is an hour out then of course British Summer time is in play

[R1Geezer]

yes jake but she's over the sea the whole time and that must be south, pretty well close to the antarctic circle i'd say which is approx 57.5 degrees south.

[jomifl]

2pm gmt @ 15 degrees per hour = 120degrees west. BST is irrelevant in this case, I arrive at 60 degrees ( give or take a few minutes|)independantly. It should also be considerered that the altitude of the plane has not been given, this would make a significant difference to the times of sunrise and sunset so I am assuming that this additional complication which I believe is a tangential function has been ignored so I'm assuming that the plane is flying at sea level.

[mike11111]

The question does not actually state that she started flying at 2 p.m. In fact the way I read it she was already in the air at that time.

[jomifl]

Mike, the time she started flying is irrelevant, what is relevant is that at dawn were she was it was 2pm GMT

[R1Geezer]

sorry make that 66.5 degrees south for the antarctic circle