» Fri Dec 16, 2011 1:36 am
I was bored too. So I decided to do my math to find out how high the Throat of the World really is. Now I may be corrected, but it is not really big. Of course I ignored the earth rotation and the air friction.
How did I do it? First I needed to find out if the gravity is equal to the one on earth (9,81 m/s2). So I used an Iron ingot and put it at the same high as my head. Then I dropped it. Within 0,99s it hit the ground. Now I got this nice little formula:
t = Root (2h / g) (h = High, g = Gravity)
I estimate my own high on 1,8m. Since I know the time and the high I can get the gravity:
(2 * 1,8) / 0,992 = 3,67 m/s2. (Well, this is some major difference from our world!)
Since I know the Gravity now, I can use the same formula to get the time of my character when he fell down the mountain (actually I used myself and the time the ingot hit the ground).
t = 9,66s
(t2 * g) / 2
= 171,23m
The mount Everest has ~8000m. So that's that.
Funny thing btw: my character hitted the ground earlier then the iron ingot (3s apart). This is a perfect example that this experiment cannot be taken seriously. In real life the volume determines how fast an object hits the ground (not the mass!). Since my body has much much more volume to interact with the air friction the iron ingot should have been there first.
(I do not claim that any of this is correct)