## What-If 0018: "B.B. Gun"

What if there was a forum for discussing these?

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ryzvonusef (1151717)
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### What-If 0018: "B.B. Gun"

http://what-if.xkcd.com/18/
In Armageddon, a NASA guy comments that a plan to shoot a laser at the asteroid is like “shooting a b.b. gun at a freight train.” What would it take to stop an out-of-control freight train using only b.b. guns?

—Charles James O'Keefe

senor_cardgage
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### Re: What-If 0017: BB Gun

I call foul on this one. The question was about an out of control freight train.

He didn't answer that question. Instead, he just mentioned the effects on a single passenger locomotive.

dotancohen
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### Re: What-If 0017: BB Gun

At t=0, 30,000 people open fire. The AK-47 typically has a 30-round magazine and fires 10 shots per second. Within a third of a second, a quarter of a million bullets are in the air.

10 bullets per second * 30,000 people * 2 rifles per person * 1/3 second = 20,000 bullets. That's off by an order of magnitude.

Red Hal
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### Re: What-If 0017: BB Gun

dotancohen wrote:
At t=0, 30,000 people open fire. The AK-47 typically has a 30-round magazine and fires 10 shots per second. Within a third of a second, a quarter of a million bullets are in the air.

10 bullets per second * 30,000 people * 2 rifles per person * 1/3 second = 20,000 bullets. That's off by an order of magnitude.

(10 * 30,000 * 2) / 3 = 200,000. You're off by an order of magnitude.
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speising
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### Re: What-If 0017: BB Gun

does anybody else find it funny that in the linked laser deflection paper the impactor is labeled "BAD ROCK" in one image?

dotancohen
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### Re: What-If 0017: BB Gun

Red Hal wrote:(10 * 30,000 * 2) / 3 = 200,000. You're off by an order of magnitude.

Hey, you're right! I hope that my faulty math hasn't found its way into any of my cod###----NO CARRIER----####

Patrik3
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### Re: What-If 0017: BB Gun

How about, 1 person, 2 heavy guns, and aim for the wheels?

ron_mega
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### Re: What-If 0017: BB Gun

According to Wikipedia, the GE Genesis weighs about 120 metric tons, not 12.

jcochran
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### Re: What-If 0017: BB Gun

Red Hal wrote:
dotancohen wrote:
At t=0, 30,000 people open fire. The AK-47 typically has a 30-round magazine and fires 10 shots per second. Within a third of a second, a quarter of a million bullets are in the air.

10 bullets per second * 30,000 people * 2 rifles per person * 1/3 second = 20,000 bullets. That's off by an order of magnitude.

(10 * 30,000 * 2) / 3 = 200,000. You're off by an order of magnitude.

And you've suffered from a fence post error.

30,000 people * 2 rifles per person = 60,000 bullets per "wave"
Waves
t = 0.0 seconds
t = 0.1 seconds
t = 0.2 seconds
t = 0.3 seconds

So within 1/3 of a second 4 waves of bullets have been launched for a total of 240,000 bullets.

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### Re: What-If 0017: BB Gun

Unless they're all the heroes of FPS, I wouldn't count on any of them dual-wielding fully automatic AK47s and still hitting the train.

I was disappointed that he treated the trains as infinitely rigid for most of time. As I understand it, supplying enough force to stop a train to just the front would cause it to fold like a house of cards.

Actually now that I think of it, derailing a train should be much more efficient than trying to counter it's momentum. Maybe they should ll be firing from the side, or at the tracks?
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zukenft
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### Re: What-If 0017: BB Gun

so you CAN destroy a train with bullets. How many bullets would we need to destroy a tank, then? how about a building?

Klear
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### Re: What-If 0017: BB Gun

zukenft wrote:so you CAN destroy a train with bullets. How many bullets would we need to destroy a tank, then? how

How many swings from a crowbar?

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### Re: What-If 0017: BB Gun

It's an imaginary train.

How thick would an imaginary wall of b.b's have to be?

Danm thick.

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Splarka
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### Re: What-If 0017: BB Gun

Quizatzhaderac wrote:Actually now that I think of it, derailing a train should be much more efficient than trying to counter it's momentum. Maybe they should ll be firing from the side, or at the tracks?

Experiments to derail trains - World War Two RailRoads & Spectacular Train Crash Documentary: http://www.youtube.com/watch?v=D-8gV4DJZUw

Not as easy as one might think.
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keithl
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### Re: What-If 0017: BB Gun

Oh, come now.

The setup clearly stated "BB gun". BB == Ball Bearing, not AK47 round. But it did not specify the size of the gun or the bearing. It did not specify "air gun". So, we have some interesting degrees of freedom here.

The largest bearings I could find with a quick google search are the seismic isolation bearings of the Benicia-Martinez Bridge. 12 foot diameter. Probably cylinder bearings (sigh), but since the cheesy article doesn't specify I will assume for fun that they are steel and round. 1.8 meter radius, 25.6 cubic meters, 200 metric tons.

And the gun? Lets assume a SHAARP hypervelocity hydrogen gas gun. My buddy John Hunter is designing these for orbital speeds, but to date he has only built 4000 m/s guns.

We need to stop a freight TRAIN, not merely a locomotive, so our round must pass through the locomotives and all the freight cars to reach the cars at the end. Yes, the vapor from the locomotives and first freight cars will be moving backwards, and fragments of the cars in back might be moving forward, but I figure we've "stopped" the train as long as the center of mass of the debris cloud ends up moving at zero velocity.

A 115 car coal train has six power units at 200 tons each, with cars loaded to 120 tons, for a total weight of 15000 tons. Assume it is moving 60 miles per hour, 26.8 meters per second. Total momentum, 400000 ton-meters/second. A 4000m/s, 200 ton ball bearing contains 800000 ton-meters per second of momentum. So if only 50% of the momentum transferred (we can assume fragments of the round will pass through the whole train without stopping) we can stop the train with one shot.

Now THAT'S a BB gun!

Of course, I could stop a freight train with an ordinary pneumatic BB gun - if I climbed in the cab and pointed it at the engineer - but where's the sport in that?

airdrik
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### Re: What-If 0017: BB Gun

keithl wrote:Oh, come now.

The setup clearly stated "BB gun". BB == Ball Bearing, not AK47 round. But it did not specify the size of the gun or the bearing. It did not specify "air gun". So, we have some interesting degrees of freedom here.

The largest bearings I could find with a quick google search are the seismic isolation bearings of the Benicia-Martinez Bridge. 12 foot diameter. Probably cylinder bearings (sigh), but since the cheesy article doesn't specify I will assume for fun that they are steel and round. 1.8 meter radius, 25.6 cubic meters, 200 metric tons.

And the gun? Lets assume a SHAARP hypervelocity hydrogen gas gun. My buddy John Hunter is designing these for orbital speeds, but to date he has only built 4000 m/s guns . We need to stop a freight TRAIN, not merely a locomotive, so our round must pass through the locomotives and all the freight cars to reach the cars at the end. Yes, the vapor from the locomotives and first freight cars will be moving backwards, and fragments of the cars in back might be moving forward, but I figure we've "stopped" the train as long as the center of mass of the debris cloud ends up moving at zero velocity.

A 115 car coal train has six power units at 200 tons each, with cars loaded to 120 tons, for a total weight of 15000 tons. Assume it is moving 60 miles per hour, 26.8 meters per second. Total momentum, 400000 ton-meters/second. A 4000m/s, 200 ton ball bearing contains 800000 ton-meters per second of momentum. So if only 50% of the momentum transferred (we can assume fragments of the round will pass through the whole train without stopping) we can stop the train with one shot.

Now THAT'S a BB gun!

Of course, I could stop a freight train with an ordinary pneumatic BB gun - if I climbed in the cab and pointed it at the engineer - but where's the sport in that?

Now that is a far superior "What if we tried More Power" follow up.
I can just imagine the gigantic BB flying down the tracks, Comparable in size to the front of the train (a little wider, a little shorter), at super high speeds as it plows through the train, throwing shrapnel in all directions.

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### Re: What-If 0017: BB Gun

keithl wrote:... I figure we've "stopped" the train as long as the center of mass of the debris cloud ends up moving at zero velocity.

Ideally, this how we'd always measure stopping power.
The thing about recursion problems is that they tend to contain other recursion problems.

Zinho
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### Re: What-If 0017: BB Gun

Klear wrote:
zukenft wrote:so you CAN destroy a train with bullets. How many bullets would we need to destroy a tank, then? how
How many swings from a crowbar?

Depends. Gordon Freeman, by himself, even rocking the HEV, is unlikely to apply enough stress to the tank's armor with a crowbar to dent it, let alone cause any damage. Adding a bunch of Gordon clones won't help the situation much, either. Randall estimated about 1% interference from rebounding BBs, with crowbars that would be significantly higher.

The real problem is material strengths. To break through an armor plate (like tank armor) you need to apply stress (load/cross-sectional area) greater than its ultimate strength. At 4+ inches thick and with an ultimate tensile strength of 100,000+ lbs/in^2 you won't be tearing tank armor with crowbar and bare hands. Plug a bunch of broad estimates into a beam stress calculator (simply supported beam, 1000lbf load, 8ftx2ft armor panel) and you'll find you're off by about three orders of magnitude. Yield strength (bend it out of shape) is in the same order of magnitude as ultimate strength (~80,000 lbs/in^2), so there's not much hope there, either. Even to make it fail in fatigue (start cracks propagating until it shatters) you'd still need to somehow get over 30,000lbs/in^2 per hit, and I don't think that's happening with hand-held crowbars, either.

Going back to AK-47s the situation doesn't get much better. I'm going to gloss over specifics (impact mechanics get messy, and I'm not prepared to write an internet treatise on the topic) and just say that when a tank's armor is rated as "effective against small arms" they mean that a bullet doesn't generate enough stress in the metal to do more than leave a small bullet-shaped impression. The impact creates local loads higher than the yield strength, but giving it the treatment Randall gave the train will be more akin to shot peening than penetration, and will likely increase the strength of the armor at its surface. I just don't think that a distributed approach will work well here.

That being said, if you were to take a few thousand crowbars, bundle them together tightly, then swing them at the tank with a crane you might be onto something. Something like that might be useful for tearing down a building, too. All things considered, though, for both tanks and buildings I'd rather use explosives.

nowhereman
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### Re: What-If 0017: BB Gun

keithl wrote: but to date he has only built 4000 m/s guns.

Comments like this are why I love the forums. I can't think of anywhere else someone can refer to a speed in excess of Mach 12 as being 'only' that fast. You have been awarded one internet.
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neremanth
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### Re: What-If 0017: BB Gun

Just being nitpicky here, but I think this is actually What-If 0018...

speising
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### Re: What-If 0017: BB Gun

keithl wrote:Oh, come now.

The setup clearly stated "BB gun". BB == Ball Bearing, not AK47 round. But it did not specify the size of the gun or the bearing. It did not specify "air gun". So, we have some interesting degrees of freedom here.

...

Nice, but, not knowing what a BB gun is, i referred to trusty wikipedia; there they state that "BB" comes from a bird shot caliber, the meaning "ball bearing" beeing more of a retronym.

Barstro
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### Re: What-If 0017: BB Gun

It's been a long time since I did any physics;

Would switching to lead pellets instead of BBs (this is still within the confines of "BB gun") result in greater or lesser stopping power due to the pellets not bouncing back at the shooters?

Does the increased mass of the train due to all the bullets or pellets (now being stuck to or inside the train) alter any of the equations provided?
Last edited by Barstro on Tue Oct 30, 2012 7:27 pm UTC, edited 1 time in total.

nowhereman
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### Re: What-If 0017: BB Gun

Barstro wrote:It's been a long time since I did any physics;

Would switching to lead pellets instead of BBs (this is still within the confines of "BB gun") result in greater or lesser stopping power due to the pellets not bouncing back at the shooters?

Does the increased mass of the train due to all the bullets or pellets alter any of the equations provided?

Answer is most likely less. While 1% of the power (Randall's estimation. I have no idea how accurate that is) is sapped due to in air collisions, the energy used in lead deformation would likely be much higher.
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jcochran
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### Re: What-If 0017: BB Gun

Barstro wrote:It's been a long time since I did any physics;

Would switching to lead pellets instead of BBs (this is still within the confines of "BB gun") result in greater or lesser stopping power due to the pellets not bouncing back at the shooters?

Does the increased mass of the train due to all the bullets or pellets alter any of the equations provided?

Hmm. Given the conservation laws, I believe you want the BBs to bounce. An impact where the BB sticks to the target will impart less momentum than one in which the BB bounces off (ideally with close to its original velocity).

ijuin
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### Re: What-If 0017: BB Gun

Let me propose another "what if we tried more power" variant: To stop the train with ONE BB, how fast would the BB it have to be traveling? (Let's use the Special Relativity calculations here and ignore the General Relativity effects of the Earth's gravity and motion. Also, let's ignore the fact that the BB would vaporize like the relativistic baseball.)

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### Re: What-If 0017: BB Gun

ijuin wrote:Let me propose another "what if we tried more power" variant: To stop the train with ONE BB, how fast would the BB it have to be traveling? (Let's use the Special Relativity calculations here and ignore the General Relativity effects of the Earth's gravity and motion. Also, let's ignore the fact that the BB would vaporize like the relativistic baseball.)

Assuming an ordinary-sized BB, you may also have to make the train invulnerable as well as the BB. An invulnerable BB with a momentum equal to that of a train would probably rip straight through the train and continue out the back side without slowing down much (and thus without slowing the train down much). So you'd need a train tough enough to stop the BB, and absorb or reflect its momentum.

Given some kind of perfectly elastic collision between an invulnerable train and an invulnerable BB, the calculation should be simple: velocitybb = velocitytrain * masstrain / massbb
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ijuin
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### Re: What-If 0017: BB Gun

That's true for Newtonian mechanics, but since the train masses hundreds of tons and the BB masses less than a gram, a pure Newtonian solution would involve the BB traveling several times faster than "c". The question is, what is the appropriate velocity under Special Relativity for matching the momentum of the train to that of the BB?

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### Re: What-If 0017: BB Gun

ron_mega wrote:According to Wikipedia, the GE Genesis weighs about 120 metric tons, not 12.

Same found in Reddit http://www.reddit.com/r/xkcd/comments/1 ... un/c6u176v
So do we have to times everything by 10 now?
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project2051
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### Re: What-If 0017: BB Gun

The next question, How many bodies do you need to throw in front of a freight train to slow it down?

Dr Frankenstein
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### Re: What-If 0017: BB Gun

This seems to be more like about stopping a passenger locomotive with no wagons. And indeed, as stated above, a GE Genesis weighs 121 tonnes, somewhat lighter than its freight cousin, the GE Evolution, at 196 tonnes (for an ES44AC).

Tiberius
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### Re: What-If 0017: BB Gun

ijuin wrote:That's true for Newtonian mechanics, but since the train masses hundreds of tons and the BB masses less than a gram, a pure Newtonian solution would involve the BB traveling several times faster than "c". The question is, what is the appropriate velocity under Special Relativity for matching the momentum of the train to that of the BB?

Well we physicists don't use F=ma for that very reason. F=dp/dt always works however. So you just have to set the newtonian momentum of the train to be equal to the relativistic momentum of the bb, p=m*\gamma*v. This yields a velocity of 0.98334 of the speed of light. Of course this assumes a perfectly inelastic collision in which the train and the bb hit each other and stop dead without the bb bouncing off. That kinetic energy has to go someplace. Further use of special relativity finds that the energy given off into the environment by the collision is 1.646×10^14 joules or 40 kilotons of tnt which is approximately 2.5 times the size of the nuclear bomb that was dropped on hiroshima. So for the good of the species don't try this at home.

keithl
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### Re: What-If 0017: BB Gun

I like the relativistic BB idea.

But I carefully re-read the problem statement, which contains the phrase: "shooting a b.b. gun at a freight train". That can be parsed two ways, either as shooting at a freight train with a b.b. gun - or - shooting the b.b. gun itself out of some larger gun at the train. So now we are dealing with a 2 kilogram (daisy 853, est.) projectile, instead of a subgram projectile. If we are still trying to stop a 15 thousand ton train moving at 60mph, or 400,000 ton-m/s, the 2kg projectile would need to move at about 170,000 km/sec (0.55 c) to stop the train by relativistic momentum alone.

However, stopping the train might be as simple as stopping the forward rolling of the locomotives, blocking the forward movement of all the subsequent cars. And coal trains would be good for this, they would probably turn into a small mountain of coal and twisted metal. I bet that if we aimed the "gun gun" properly, we could drop a locomotive down to the ties, wedging it into the ground. Train wheel diameters are about a meter, so dropping everything above the axle down to the roadbed will take on the order of 300 milliseconds. Perhaps if we can make a good portion of the top of the locomotive spall skywards, we can get additional vertical thrust and slam it into the roadbed quicker. However, a mile long coal train rolling freely at 60mph will still need about a minute to finish piling up.

But train won't roll freely. In fact, a train is stopped by air brakes, and if a brake coupler hose ruptures and loses pressure, all the cars brake to a stop automatically.

So all our momentum calculations are beside the point!

If you can use your b.b. gun to puncture a brake coupling hose, the whole train will brake to a stop. And it probably wouldn't take all that much gun enhancement to shoot an ordinary b.b. fast enough to penetrate a hose. One of the Drozd tactical B.B. machine guns could probably shred a hose if accurately aimed at one spot on a brake coupler hose as it moves past.

There I go, spoiling ALL the fun.

Tiak
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### Re: What-If 0017: BB Gun

The proposed purpose of the laser would be to deflect the asteroid, not stop it. The equivalent should be the number of BBs to derail a train if aimed by precise automation.

Bloopy
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### Re: What-If 0017: BB Gun

keithl wrote:A 115 car coal train has six power units at 200 tons each, with cars loaded to 120 tons, for a total weight of 15000 tons. Assume it is moving 60 miles per hour, 26.8 meters per second. Total momentum, 400000 ton-meters/second. A 4000m/s, 200 ton ball bearing contains 800000 ton-meters per second of momentum. So if only 50% of the momentum transferred (we can assume fragments of the round will pass through the whole train without stopping) we can stop the train with one shot.

Now THAT'S a BB gun!

So, scaling that ratio up, you'd need to find an asteroid with about 1/4 the diameter of the one you're trying to stop, and slingshot it to 150x the speed for collision.

"Ah, crap."

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### Re: What-If 0017: BB Gun

Wait, I'm still stuck on the first step. If the train weighs 12 metric tons (12,000 kilograms) and is going 45m/s, firing a single BB (0.33g, or 0.00033kg, 100 m/s) would cause an impact with a total speed of 145m/s.
The train's initial momentum was 540,000 kgm/s.
The bb impact would reduce its momentum by 0.00033 * 145 = 0.04785 kgm/s.
Each additional BB would slow it down by slightly less (since the train would have slowed slightly, causing the next BB impact to have slightly less momentum), but even if we were to assume that every bb impact reduced the train's momentum by the same 0.04785kgm/s, it would take 540,000 / 0.04785 = 11,285,266 bbs to stop the train.

Randal says it would take only 200,000. Where is my math screwed up?
Last edited by bugbread on Wed Oct 31, 2012 8:28 am UTC, edited 1 time in total.

Istaro
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### Re: What-If 0017: BB Gun

So far I have enjoyed this thread even more than the original post (no offense, Randall, it's a testament to the intellect of the fans you attract).

rkratky
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### Re: What-If 0017: BB Gun

I would be interested in reading about the effects of the heat generated by all those people firing AK-47s so close together. Considering the number of shots fired at the same time, would it even be (theoretically) possible to fire more than a few rounds?

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### Re: What-If 0017: BB Gun

bugbread wrote:Randal says it would take only 200,000. Where is my math screwed up?

Randal did the major screw up, while some different assumptions give different numbers there is no way to get even close to 200 000 bullets, and thus 2 days of shooting is also wrong.

If you suppose perfect bounceback, and account for the decreased effectivity as the train slows, it would take 6 755 701 0.33g bullets fired at 100 m/s to stop a 12 000 000g train running 45 m/s.
Assuming no bounce back the number would be doubled to 13 511 402.
Further assume that the bullets are stuck in the train and thus increase the trains mass gradually and you get 16 363 636 bullets.

All these numbers would have to be multiplied by 10 to stop a real 120 000 000g locomotive.

cellocgw
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### Re: What-If 0017: BB Gun

nowhereman wrote:
keithl wrote: but to date he has only built 4000 m/s guns.

Comments like this are why I love the forums. I can't think of anywhere else someone can refer to a speed in excess of Mach 12 as being 'only' that fast. You have been awarded one internet.

To save everyone's brain strain, the wikipedia value for escape velocity (on earth) is 11.2 km/s . So he's got a ways to go.
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cellocgw
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### Re: What-If 0017: BB Gun

project2051 wrote:The next question, How many bodies do you need to throw in front of a freight train to slow it down?

Correction: how many *moles* ...
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