This is a very interesting question. Just for your knowledge, the
deepest point of all the four oceans is in the Pacific Ocean. It's
called the Mariana Trench, and it's 36,198 feet deep. So, if you put
Mt. Everest in it, there would still be 1.4 miles of water above it!
So, since 1 foot = .3048 meters, 36,198 feet = 11,033.15 meters.
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This first calculation below will neglect air resistance. This
will give us an answer that is too short, because the air will slow
down the falling person.
Now, we will just use an equation:
Distance = (initial velocity)(time) + (.5)(acceleration)(time^2)
Since the human is going to be dropped from the top of the trench,
its initial velocity, or speed, is zero. And zero times anything is
still zero.
So NOW the equation is:
Distance = (.5)(acceleration)(time^2)
We know the acceleration because it is due to the force of gravity.
This value is equal to 9.8 m/s^2. And we also know the distance, which
is the vertical distance of the trench. So-----now we solve!
11,033.15 = (.5)(9.8)(time^2)
2,251.663 = (time^2)
47.45 seconds = time!
Can you believe it takes 45 seconds to fall down to the bottom of that thing? Well, it doesn't.
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Doing a quick job with air resistance, we note that the force due
to air friction increases with the speed something is falling, while
the force due to gravity remains constant. Eventually, the person will
speed up until the two forces cancel. This is called "Terminal
Velocity", and is approximatley 200 mph for a person falling unaided
through the air. It depends very much on whether the person is
spreading his/her arms out, or is pointed down like a diver at the
pool, or whether he/she is wearing a parachute (and whether it is open
or not!). A person fallign with the aid of a parachute will even
survive this drop and take a lot longer.
Assuming no parachute, at 200 mph it will take about 2 minutes to
reach the bottom, give or take some. Not a long lease on life!
Well, hopefully you understood what was going on. I hope this helped!
(published on 10/22/2007)
