Correction to the above: the person is 75 kilograms, not meters, and the sphere is 60 kilograms per meter, not pounds.
Q.E.D. is technically right – if you start from any finite distance, you will not technically reach escape velocity through a free fall, unless you have an initial velocity. This is because escape velocity is defined as the velocity one would need to have at the surface of the planet to escape the effects of gravity, which means travel from the surface to an infinite distance away. So due to the way e.v. is defined, you can only reach it in a free fall if you start from infinity.
However, for all practical purposes, if you start from a large enough distance away (far enough that the force of gravity due to the planet is very very weak), your velocity right before impact will be very close to the escape velocity, and may very well be equal to the escape velocity within the precision of your measurement.
So i think the disagreement here is really a question of semantics.
theckhd, I agree it is a question of semantics. My problem is that even taking the idea that you never reach escape velocity (actually you would reach it exactly if you started an infinite distance away with nothing else in the universe, so we will say it can never quite be reached), you do not aproach it asymptotically. You have a curve that, if you extended it to the point of impact (or miniscully beyond) would cross the escape velocity in a simple manner. No limit need be taken, it does not approach this value (or line if you go with the more general definition), it reaches it at a time point just out of consideration.
snailboy, I would not fworry about running the equations with a ball based on the zorb, you would be doomed. The thing pop and squish you. Anything that would be able to absorb the impact would be a LOT heavier. We need to come up with a design… and a volunteer.
I think that you and Q.E.D. are talking about different things.
You’re right if you’re stating that the velocity wouldn’t approached the escape velocity asymptotically during a single free fall. The slope of a velocity vs. **time ** graph for the fall would most certainly not look like it was asymptotically approaching the escape velocity. This is the reason i say it’s not really fair to call the escape velocity a “terminal velocity” in the common sense, because the two terms refer to very different behavior in time (terminal velocity does asymptotically approach a certain value on a velocity vs. time graph).
Q.E.D. didn’t claim otherwise in his first post though. What he said was:
So he’s looking at a plot of final velocity vs. fall distance, which would asymptotically approach the escape velocity as fall distance (which is your initial ‘height’, not your instantaneous position) approached infinity. This makes sense, since the force on the falling object is so ridiculously weak once you start from a great enough distance that a slight displacement in the object before allowing it to start free fall will make smaller differences in the final velocity as the initial height of the object incereases.
So when he said that it was reversible, I assumed he was still referring to his velocity vs. fall distance relationship, not a velocity vs. time graph (because if he was referring to a velocity vs. time graph, he’d be wrong).
I don’t think he ever meant to imply otherwise, but this conversation has been confusing enough (at least in what particlar behavior or “plot” people ar referring to) that I can see how we got mixed up. So you’re both right, and your statements are not mutually exclusive, they both describe the phenomenon properly when looking at the problem from their respective points of view.
Anyway, i think we all agree with you that our mass estimates are gross under-estimates for a ball that could survive the impact. If you come up with the design, i’ll volunteer snailboy to be the test pilot. 
That’s exactly what I was saying. You put it better than I did, however. Thank you.
Whether the design is like the Zorb’s or not, the mass of it will still be dependant on the size, so I just can’t make sense of assuming a certain mass when calculating the size.
And you made me understand. You are absolutely right, Q.E.D..
Absolutely, the mass will depend upon the size, but the function will be dependent on the design. The largest weight would probably be in the external sphere (which has to hold up to the huge impulse due to its own momentum on impact along with the distributed forces from holding the interior sphere as it decelerates). Thus, the weight will depend upon the surface area and go up with r^2 if not r^3.
The only problem I see with falling from a sealed ball is you loose the thrill of the jump.
First you get strapped inside giant ball, kicked out of a plane, freefall for a short time, then hit the ground at 100 mph. What’s the thrill in that?
You can have the same effect by getting into the giant ball and having your friend mash into it with their SUV.
The ball would need to be something you can see out of. Somehow see the ground coming at you doing 100mph.
Dunno. It sounds like a blast to me. But I want it tested with a dummy before I climb in. I like the maths you guys have demonstrated. It is a long time since I did any fluid mechanics and I don’t have a lot to add. Except to say that the easiest way of factoring in the mass of the sphere itself would be to perform an iterative calculation. Real engineers would include a factor of safety into the whole thing too.
One thing that no one has mentioned is what happens after you land. That Zorb is going to bounce! A pure elastic collision (ok we won’t get that) is going to double the total impact force. Acceleration should be around the same since it will take the same time for the bounce up action as it did for the landing part. I’m just not sure I want to be experiencing 10 Gs for 1.4 seconds as suggested by flight.
One could always add to the fun by landing on a slope or hillside of some sort. Now, there’s a ride for you.
You put your hampster in an opaque ball? Is that some kind of Goth hampster? Personally I’ve been visualising using a transparent ball the whole time.
As an aside, in the Judge Dredd stories from 2000 AD comics, one of the many banned recreational activities of Megacity One was to embed yourself in a clear ball of “Boing” (the miracle plastic!) and go for a bounce off the highest building you could find.
Ditto on the assuming it was a clear ball. What would be the point, otherwise?
It wouldn’t really be a pure elastic collision, would it? The internal bungy support system would, presumably, or could be designed to, use up much of the energy.