## How high to drop water balloon from for it to be deadly

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Helmanex
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### How high to drop water balloon from for it to be deadly

Someone asked this question to my teacher. He later emailed us all with a response;

"I don't think any height could cause a death by water balloon! At least, not for a small balloon. Here's my back-of-the-envelope calculation to that effect:
I assumed a spherical water balloon weighing about 1 kg (that is, a few pounds), and after a quick calculation, I worked out that the terminal velocity of the water balloon is about 50 m/s.

How much force does that transfer to the person? Well, the change in momentum will be something less than (mass)*(velocity), because clearly not all of the water will just come to a complete stop on top of your head (most of it will splash and continue going down, right?) Still, to be conservative let's say 2/3 of the mass comes to a complete stop on your head, so the impulse = change in momentum times 2/3:
I = 2/3*(50 m/s)*(1 kg) =33.333 kg m/s

Now, the average force will be I/(time duration of impact. What should we use for the time of impact? I have no idea! But let's come up with a reasonable guess. So, Let's say the impact only lasts for .1 seconds. Or, to make it even scarier, how about .075 seconds.

So, then, the average force will be I/(.075 s):

F = 444.4 Newtons.

That seems like a lot. How will we know whether that's enough force to kill? Well, our good friends at the National Highway and Safety Administration have come up with some estimates (see various reports at http://www-nrd.nhtsa.dot.gov/department ... rauma.html) about the sudden impact forces a human can withstand. As it turns out, they estimate ranges for average males, females, and children, and came up with a fatality value of about 65g if the impact is taken to the chest, side, back, or head. Let's lower that to 50g just to be on the safe side:
50g = 490 Newtons.

So, we see that the average force from a terminal velocity water balloon is not equal to the ability of the human head to withstand force!"

My question is, is it still TECHNICALLY POSSIBLE to make a water balloon have lethal speed by setting up any kind of system?

Helmanex
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### Re: How high to drop water balloon from for it to be deadly

Oh I emailed him back this possibility.

Suppose a person standing on the ground had the open end of a wide, rigid tube placed on their head firmly, with sealant such that there is an air-tight seal between his head and the tube. A few inches above his head (within the tube) there is a sheet of glass that isolates a small area within the tunnel, which lies between the glass and his head. The pressure in this area is 1 atm. BUT, above the sheet of glass, air is sucked out by pumps such that there is basically a vacuum for the immense length of tubing that extends beyond the part where there is glass inside. Stay with me now.

Since the area b/w the mans head and the glass is 1 atm, the vacuum does not cause his head to explode or boil. Now this long tube (which is roughly the diameter of a mans head) is so long that a water balloon can be dropped from the other end and can accelerate downwards to incredible speeds as it encounters no air resistance. (Lets assume the dropping mechanism up top is air tight and maintains the vacuum). Also, to ensure that the water inside the balloon doesn't boil from the vacuum, the water balloon would also be airtight. The tube can extend from the top of the mans head all the way to the outer edge of Earth's atmosphere, where gravity still has a grasp. The balloon may also be sent down by a guide wire or well-lubricate rail system to make sure it doesn't hit the sides and break. AND of course, there is some system in place to make sure the tunnel/tube stays balanced atop the mans head. Guy wires, jets, something.

In order for the balloon to have 500 Newtons of punch, it would need an I= 37.5, and thus a speed of 56.25m/s.

so ∆h = 56.25^2/(2*9.8) = 161.4 meters. Totally doable.

And just to clarify, there is a system in place such that the man can bear the weight of the tube on his head (maybe it's attached to a tower). Also, the sheet of glass is thin enough that the balloon can break through it without popping. If thats possible. Anyway, I think it IS POSSIBLE for a water balloon to be deadly. Unless I got something terribly wrong.

What do you guys think?

Geekthras
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### Re: How high to drop water balloon from for it to be deadly

Wouldn't the balloon asplode due to different pressures?

I would say that you could try using tape to pull the sides back and maybe decrease air resistance by a bit, or try it at like 15000 feet.
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Helmanex
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### Re: How high to drop water balloon from for it to be deadly

would it? even if it was air-tight? what if the balloon were made of a thin, rigid shell?
I guess thats not a water balloon anymore then

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### Re: How high to drop water balloon from for it to be deadly

for practical application, the strength of the material the balloon is made of and the pressure of the water it contains becomes relevant.

I imagine, unless the balloon is made of unobtanium, that the balloon will first deform greatly, reducing the average force of impact, and then the balloon will asplode, again reducing average force of impact.

A High-school physics balloon could be deadly, but a real life one could not.
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### Re: How high to drop water balloon from for it to be deadly

"In high-school physics, the earth is flat, wind is nonexistant, there is no air resistance, things don't break, and above all, experiments don't work."

-Me.

I heard this one a while back:
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Gelsamel
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### Re: How high to drop water balloon from for it to be deadly

.075 sounds like a ridiculous over estimate for stopping 2/3rds of the mass of a balloon traveling at 50m/s.

I doubt even if you forcibly accelerated a balloon to a higher speed it would kill you.

Edit: I mean over estimate force wise... it should be much higher.
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po2141
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### Re: How high to drop water balloon from for it to be deadly

I saw a viseo on break.com once of some college kids dropping a water balloon the size of a small fridge (about 50-100L is my guess) from the top of a building (looked like 2nd or 3rd floor) onto a hapless passer by. They survived the direct hit though it didnt look pleasant for them.

I think much less than 2/3 of the momentum is transferred to the head. Obviously in the example above much MUCH less than 2/3 was transferred because the balloon was so large (and 2/3 of (say) 50kg travelling at (say) 10m/s with an impact duration of (say) 0.1s is still 333g's)
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### Re: How high to drop water balloon from for it to be deadly

You could have just said "drop the balloon in a vacuum."

Anything is deadly at high enough velocity, even air molecules. Water has an interesting property where if the impact happens at a high enough velocity, it will essentially feel like a solid.
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Gelsamel
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### Re: How high to drop water balloon from for it to be deadly

Are you saying water is non-newtonian?
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### Re: How high to drop water balloon from for it to be deadly

Solt wrote:You could have just said "drop the balloon in a vacuum."

Anything is deadly at high enough velocity...

really, how come all these photons hitting me don't kill me then?
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po2141
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### Re: How high to drop water balloon from for it to be deadly

evilbeanfiend wrote:
Solt wrote:You could have just said "drop the balloon in a vacuum."

Anything is deadly at high enough velocity...

really, how come all these photons hitting me don't kill me then?

UV rays causing DNA damage in the skin resulting an a malignant melanoma?
Gamma rays from background radiation, or more excitingly cosmic rays penetrating the body and causing internal cancers?

Also, hypothetically, a laser-death-beam slicing you into little pieces?
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### Re: How high to drop water balloon from for it to be deadly

yes but all these low frequency photons hitting me aren't coherent or high enough energy so don't hurt me in the slightest, yet they move at the same velocity as the dangerous, high frequency ones. i.e. its not just about velocity on its own, you have to consider momentum and/or energy.
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Helmanex
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### Re: How high to drop water balloon from for it to be deadly

Solt wrote:You could have just said "drop the balloon in a vacuum."

I tried to be elaborate to make it more convincing that setting up such a system would be plausible. But I'm starting to think it's not because of several things I stupidly assumed.
For instance, if you take a person's head to be, say, a 20 cm by cm square, the glass must actually be quite strong: it is capable of holding a pressure of 1 atm between the head and itself, while on the other side of the glass is a vacuum, so, no pressure at all. That means that glass is resisting an upwards force of 1 atm/((.2 m)^2)by keeping an atmospheric pressure near the man's head. Converted into Newtons (1 atm is about 101 Newtons), that means the balloon is falling against a sheet of glass supported by a force of F = 2525 Newtons (basically, when the balloon breaks through the glass, there will be a massive but short rush of air as the pressure suddenly equilibrates in the tube). Anyway, that force is nothing to sneeze at, and certainly not something to just drop from the calculation.

Also, I guess the water inside the balloon would boil while in the vacuum tube (or is this incorrect?), or at least expand the balloon greatly.

So I guess it is IMPOSSIBLE for someone to die (get hit with ~500N of force) by the falling of a normal-sized water balloon. *sigh*

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### Re: How high to drop water balloon from for it to be deadly

Freeze it first. Then 2/3rds of the force isn't wasted, resulting in a leathal impact. And it's still technically a "water balloon", because you didn't specify what phase the water had to be in.

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### Re: How high to drop water balloon from for it to be deadly

Neuman wrote:Freeze it first. Then 2/3rds of the force isn't wasted, resulting in a leathal impact. And it's still technically a "water balloon", because you didn't specify what phase the water had to be in.

What do I win for pointing out the obvious solution?

You beat me. I was just about to suggest freezing.

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### Re: How high to drop water balloon from for it to be deadly

Of course water is newtonian. Ideal newtonian fluids can't support shear forces, water can. It's this effect that makes it feel like a solid, it's not that the water is non-newtonian, it's that at high speeds it can't flow away fast enough to feel like a liquid. Good thing too, or or swimming would be very difficult. As for the death balloon, dropping it from far enough away in a vacuum would work. Anything with sufficient momentum and energy can kill you. Alternatively, if you don't like the vacuum idea, move your subject to a higher acceleration gravitational field than the assumed earths field. That'll work pretty well too.

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### Re: How high to drop water balloon from for it to be deadly

actually, using vacuum or higher acceleration frame wouldn't work because the materials the balloon is made of will fail before the water balloon becomes deadly and in a manner that will prevent deadly force from being transferred.

Eventually, you get high enough velocities that even the very small percentage of force applied to the target is deadly, but by then I'm not sure we're talking as much about a water balloon as any relatively cohesive matter stream
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### Re: How high to drop water balloon from for it to be deadly

We have a very large balloon filled with water, suspended at whatever height would cause water to accelerate to terminal velocity. It has a slow leak. drip... drip... drip... onto that poor guy's head, in the same spot, over and over. It would eventually bore a hole into his head. Once the balloon is empty, the balloon falls onto his lifeless body. And there you have it, a deadly water balloon.

Gelsamel
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### Re: How high to drop water balloon from for it to be deadly

That would do naught but torture him. Impact time is a major consideration in this. Spreading the momentum of the whole balloon over like a hours will do shit all. It's like saying I can punch my first though you if I apply a small pressure on you for a day or so.
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Helmanex
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### Re: How high to drop water balloon from for it to be deadly

Neuman wrote:Freeze it first. Then 2/3rds of the force isn't wasted, resulting in a leathal impact. And it's still technically a "water balloon", because you didn't specify what phase the water had to be in.

I suppose I should've defined what a water balloon is first: A balloon made from some stretchy material, about the size of a persons hand, filled with (liquid) water. A regular 'ol water balloon. And this dropping is to take place on Earth.

So does anyone have an idea as to how to make a falling water balloon impact with deadly force? Simply dropping it in a vacuum tube wouldn't work, because of various complications as described above.

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### Re: How high to drop water balloon from for it to be deadly

It's almost impossible unless you have a way of significantly increasing impulse.
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### Re: How high to drop water balloon from for it to be deadly

With a regular ballon i dont think it would be possible, but if you got some different ballon, made of a harder material then I think it could be done.

I'm not sure of this since I know just the basics of fluid drag but I think a harder material would be more "aerodynamic", because it would remain in it's form. And besides, if it is fragile, it would reduce the time of impact, aplying a bigger force.
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### Re: How high to drop water balloon from for it to be deadly

How about if we have the guy fall head-first on the balloon? That would kill him, no?

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### Re: How high to drop water balloon from for it to be deadly

Gelsamel wrote:Are you saying water is non-newtonian?

nilkemorya wrote:Of course water is newtonian. Ideal newtonian fluids can't support shear forces, water can. It's this effect that makes it feel like a solid, it's not that the water is non-newtonian, it's that at high speeds it can't flow away fast enough to feel like a liquid. Good thing too, or or swimming would be very difficult.

Thank you nilkemorya.

evilbeanfiend wrote:
Solt wrote:You could have just said "drop the balloon in a vacuum."

Anything is deadly at high enough velocity...

really, how come all these photons hitting me don't kill me then?

Wow, you don't have to be pedantic about it. I never said anything about mass or momentum. Anything with mass and in high enough quantities and at high enough velocity is deadly.

Helmanex wrote:
Solt wrote:You could have just said "drop the balloon in a vacuum."

I tried to be elaborate to make it more convincing that setting up such a system would be plausible. But I'm starting to think it's not because of several things I stupidly assumed.
For instance, if you take a person's head to be, say, a 20 cm by cm square, the glass must actually be quite strong: it is capable of holding a pressure of 1 atm between the head and itself, while on the other side of the glass is a vacuum, so, no pressure at all. That means that glass is resisting an upwards force of 1 atm/((.2 m)^2)by keeping an atmospheric pressure near the man's head. Converted into Newtons (1 atm is about 101 Newtons)

Actually 1 atm is 101,300 Pascals or 101,300 Newtons per square meter putting a force of about 4,000 Newtons or 400 kg on the glass. This is not a problem since even the very first space vessels had windows.

, that means the balloon is falling against a sheet of glass supported by a force of F = 2525 Newtons (basically, when the balloon breaks through the glass, there will be a massive but short rush of air as the pressure suddenly equilibrates in the tube). Anyway, that force is nothing to sneeze at, and certainly not something to just drop from the calculation.

The simple way to get around this would be to just use a block thick enough to transmit the force without itself shattering, and keep the block in contact with the dude's head from the beginning. Although, if you're going to modify things like this you might as well take it a step further and put something like a solid cone on his head (with the very sharp point touching, and the balloon falling on the big flat side). Then the pressure on contact would be enormous enough to do all manner of ridiculously gory things. Or you just wouldn't need as high a drop. Hell, you could do it in a regular atmosphere, no vacuum needed.

Hey, I found a better solution.

Also, I guess the water inside the balloon would boil while in the vacuum tube (or is this incorrect?), or at least expand the balloon greatly.

I'm not entirely sure what would happen. I think the vacuum would cause expansion of the balloon and as a result vaporization of the outer layers of the water globule. However, after enough vaporization took place the water temperature would drop and it would freeze over. So you'd have some "snow" and a solid ball of ice. And a ruptured balloon skin. In any case, if you use the above method you circumvent this question since you don't need a vacuum.

So I guess it is IMPOSSIBLE for someone to die (get hit with ~500N of force) by the falling of a normal-sized water balloon. *sigh*

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Helmanex
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### Re: How high to drop water balloon from for it to be deadly

Solt wrote:The simple way to get around this would be to just use a block thick enough to transmit the force without itself shattering, and keep the block in contact with the dude's head from the beginning. Although, if you're going to modify things like this you might as well take it a step further and put something like a solid cone on his head (with the very sharp point touching, and the balloon falling on the big flat side). Then the pressure on contact would be enormous enough to do all manner of ridiculously gory things. Or you just wouldn't need as high a drop. Hell, you could do it in a regular atmosphere, no vacuum needed.

Using a cone as described would be stepping away quite a bit from the idea of having a man die by the impact of a water balloon. I mean, might as well make it a knife instead of a cone then. Or have the falling balloon trigger a Rube-Goldberg device that blasts him in the face with a shotgun. Point is, he must be killed directly by the balloon.
Thank you for your amendments to my calculations.

Anyway, after pondering about this for a bit, and reading some of the stuff here, it seems more and more impossible. Myth busted (?)

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### Re: How high to drop water balloon from for it to be deadly

So if you can't freeze it, can you start with it high enough so that it freezes? Certainly no one has ever been killed by a hailstone before...

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### Re: How high to drop water balloon from for it to be deadly

Can the balloon not contain a shard of glass or something inside it? The specification does not once mention that the balloon must only be made up of the balloon skin (presumably rubber) and water molecules...
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### Re: How high to drop water balloon from for it to be deadly

Solt wrote:Nothing is impossible! With the right tools (math and physics) we can make anything happen!

Exactly.

Now let's begin: Assume a perfectly spherical balloon falls through the air, and remains spherical for the duration of the fall. Assume zero air resistance.

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### Re: How high to drop water balloon from for it to be deadly

No.. we can't even make everything hypothetically happen, like perfectly rigid bodies.
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### Re: How high to drop water balloon from for it to be deadly

mathmagic wrote:
Solt wrote:Nothing is impossible! With the right tools (math and physics) we can make anything happen!

Exactly.

Now let's begin: Assume a perfectly spherical balloon falls through the air, and remains spherical for the duration of the fall. Assume zero air resistance.

You can't assume that, he already told us that the terminal velocity for the ballon is 50m/s.

Of course that with asuming zero air resistance it could be done, you just drop it from 10 kilometers high and it's done
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### Re: How high to drop water balloon from for it to be deadly

Govalant wrote:
mathmagic wrote:
Solt wrote:Nothing is impossible! With the right tools (math and physics) we can make anything happen!

Exactly.

Now let's begin: Assume a perfectly spherical balloon falls through the air, and remains spherical for the duration of the fall. Assume zero air resistance.

You can't assume that, he already told us that the terminal velocity for the ballon is 50m/s.

Of course that with asuming zero air resistance it could be done, you just drop it from 10 kilometers high and it's done

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### Re: How high to drop water balloon from for it to be deadly

Am I the only one who sees this not as an interesing physics problem, but affirmation that the original poster has a cool physiscs teacher?

He took the time to analyse the problem and reply to a student's off hand question.

Very nice.

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### Re: How high to drop water balloon from for it to be deadly

Title for Govalant: Doesn't get jokes.

Okay I'm an idiot. Sorry.
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### Re: How high to drop water balloon from for it to be deadly

Tom Jr wrote:Am I the only one who sees this not as an interesing physics problem, but affirmation that the original poster has a cool physiscs teacher?

He took the time to analyse the problem and reply to a student's off hand question.

Very nice.

Not to mention he answered the same question as asked. I think ~80% of the answers I've gotten from professors have really been answers to slightly (or sometimes less slightly) different questions. Then again, college professors are apparently there because they hate teaching, and hate people even more.
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### Re: How high to drop water balloon from for it to be deadly

Tom Jr wrote:Am I the only one who sees this not as an interesing physics problem, but affirmation that the original poster has a cool physiscs teacher?

He took the time to analyse the problem and reply to a student's off hand question.

Very nice.

Actually he isn't my professor, but my TA for the "discussion" section of our 500 person lecture. He is a grad student in physics. But yeah, he's a really cool guy
This question came up because he had lost a bet the other week and had a water balloon dropped onto his head from 4 stories above in one of our main Physics buildings. He invited students to come watch.
(He came out physically unscathed, but pretty wet.)

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### Re: How high to drop water balloon from for it to be deadly

There is a video floating around of some kids who get a huge water balloon (almost the size of a bean bag chair) and throw it off the top of a building (maybe 4-5 stories up) onto a port-a-potty. It demolished the roof.

I'm pretty sure that could kill someone. Either it would slam them into the ground, causing serious damage, or if the rubber was still thick enough that it wouldn't break upon impact on a person's head, it could easily break someone's neck.
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### Re: How high to drop water balloon from for it to be deadly

What if there happens to be a powerful water balloon launcher 10 feet above the persons head, that accelerates the balloon to a very high velocity. Does that count as "falling"?

Or, even if the water balloon can't kill by impact, you could always drown a person with a large enough one, right?

pr1mu5
Posts: 74
Joined: Fri Sep 28, 2007 4:19 pm UTC
Location: Florida

### Re: How high to drop water balloon from for it to be deadly

Helmanex wrote:My question is, is it still TECHNICALLY POSSIBLE to make a water balloon have lethal speed by setting up any kind of system?

I'll cheat:

Drop the waterballoon from, oh, 150,000 feet. It'll freeze from the coldness/vacuum of space, and (probably) won't fully melt before hitting someone on the head on Earth.

I'll leave it to the other (smarter) people to prove whether or not a water balloon can fully freeze at that altitude before heating up from friction of air while falling and the temperature of the geographic area where you're dropping the balloon. (We don't get snow in Florida, but we do get hailstones, so I imagine this is possible)

zenten
Posts: 3799
Joined: Fri Jun 22, 2007 7:42 am UTC

### Re: How high to drop water balloon from for it to be deadly

pr1mu5 wrote:
Helmanex wrote:My question is, is it still TECHNICALLY POSSIBLE to make a water balloon have lethal speed by setting up any kind of system?

I'll cheat:

Drop the waterballoon from, oh, 150,000 feet. It'll freeze from the coldness/vacuum of space, and (probably) won't fully melt before hitting someone on the head on Earth.

I'll leave it to the other (smarter) people to prove whether or not a water balloon can fully freeze at that altitude before heating up from friction of air while falling and the temperature of the geographic area where you're dropping the balloon. (We don't get snow in Florida, but we do get hailstones, so I imagine this is possible)

You could also drop the water balloon from a distance *much* higher. It won't have time to slow down from air resistance because it's going so fast.