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Q & A: The deepest ocean...

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Most recent answer: 10/22/2007
Q:
If all of the water in the oceans disappeared, how long would it take for a human to fall to the bottom of the deepest ocean? THANKS!!
- Jessica (age 14)
St. Louis, Missouri, USA
A:
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)

Follow-Up #1: empty oceans

Q:
This answer is misleading because it neglects the change in buoyancy as the object falls through the increasingly high water pressure. It would take a very long time for a human to reach the bottom of the ocean
- MJ (age 30)
Ohio
A:
Perhaps you misread the original question:

"If all of the water in the oceans disappeared, how long would it take for a human to fall to the bottom of the deepest ocean? "

There is no water involved in the answer.

LeeH

(published on 10/22/2007)

Follow-up on this answer.