Martin answers:

Since 70% of heat loss is thru the head, make sure you sleep with a good headcover, a wool watch cap works fine. Sleep in thermal underwear, with heavy socks. Use a good sleeping bag rated for the temps you expect to encounter. As for heaters, a plug into the dash heater would drain your battery in less than an hour. Propane or other gas heaters are dangerous in enclosed spaces as they suck up the oxygen and put off toxic fumes. A proper wall heater installed with proper vents is an option, but very expensive. Heat packs from any camping outlet, placed in your sleeping bag will also keep you toasty, but your gonna fog up and ice up the inside of your windows with your breath during the night.
Check with camping world, or other camp supply stores to see what may be new on the market and safe to use.
Good luck

Martin answers:

First you have to break them down into x and y- components.

So
x-component of her walking 25.5km = 25.5 cos 35 degrees
= 20.9
x- component of her walking 41km = 41 cos 65 degrees
= 17.3

add them both together to get your resultant displacement’s x value.
20.9 + 17.3
= 38.2

Now for y- component
y- component of her walking 25.5 = 25.5 sin 35 degrees
= – 14.6 ( since it’s underneath the y-axis therefore is negative)
y- component of her walking 41 = 41 sin 65 degrees
= 37.2

Add the together
-14.6 + 37.2 = 22.6

Now to find the resultant displacement we need to use Pythagorean theorem.

Resultant displacement = sqrt(22.6^2 + 38.2^2)
=44.4
Therfore, the resultant dispalcement is 44.4km

Now the degrees would be

tan-1 Θ = 22.6 / 38.2
Θ = 37 degrees

final answer would be:
44.4km [E 37 degrees N]

Martin answers:

Hey~
I had some of my own ideas but many of them and more are covered in the sites below.
If I believe I am going to get cold, I always have a stocking cap to put on because that is where you loose your heat. I wear at least 1 full thin layer; long john’s or sweats, long sleeved t-shirt. I keep another layer in my bag to put on just in case. I think the idea of having minimal clothes is not to sweat, then get chilled and also to not fill all the airspace up in the bag.
Don’t cover your head with the sleeping bag if you get cold because your breath holds a lot of moisture that will chill you in the long run.
Oh yeah…sometimes I will do jumping jacks or run in place just before I get in my bag to create body warmth. This helps a lot. (don’t get sweaty)
Sorry the only documentation I have is Many, many years of camping and some winter camping.

Http://www.chiff.com/a/camping-sleep-warm.htm

http://www.ehow.com/how_1790_stay-warm-sleeping.html

God luck and try to stay warm!!

Martin answers:

Two ways to do this

1) R = sqrt(Rx^2 +Ry^2 +Rz^2)
R = sqrt((-2710)^2 +3810^2 +2700^2) = 5399 m

2) R = sqrt(Rr^2 +Rz^2)
R = sqrt( 4680^2 +2700^2) =5403

This is just the pythagorean theorem in three dimensions
The difference in the results is round off error.