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It's been 21 years Ms. Frizzle has been doing her best to educate the masses. Even with all the knowledge available provided on the internet, not only do people not take advantage, they choose to remain ignorant of as much as possible, preferring sound bites that have nothing to do with facts. She has had enough. She plans to teach one last lesson to her students and everyone else. It's one everyone WILL learn (for however little time it takes).

She blames the US as the center of ignorance movement and as such wants to wipe out everyone there. What she has is a special magical schoolbus that can swim through oceans and fly into space, 10 elementary students and her commitment to see this through. How fast does she have to be traveling in the bus and where in the US does she need to target in order to be able to wipe out %95-99+ of all people in the continental US? I'm guessing the aim would be somewhere in Kansas or maybe Colorado.

This is a hard science question.

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This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

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    $\begingroup$ So she is turning the magic school bus into a kinetic projectile? Bahahahaha...I read one of those books to my 5 year old last night. Also...just have it turn into a really large crop duster that leaves an ammonia cloud in its wake. $\endgroup$ – James Aug 18 '15 at 14:06
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    $\begingroup$ Also...I want to write that children's book $\endgroup$ – James Aug 18 '15 at 14:07
  • $\begingroup$ @James your question inspired this one. I might just have to try writing it too! $\endgroup$ – bowlturner Aug 18 '15 at 14:11
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    $\begingroup$ @FihanoLeSugg true, but that isn't a problem. $\endgroup$ – bowlturner Aug 18 '15 at 14:24
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    $\begingroup$ Obligatory XKCD article: what-if.xkcd.com/1 $\endgroup$ – Steve Aug 18 '15 at 17:42
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So...what this question is asking is this. At what velocity does a schoolbus need to go in order to, on impact, cause an extinction event that takes out the US. So, ultimately, this is a projectile physics question.

Note: I am assuming she wants them killed quickly, rather than letting them die out in a nuclear winter, which humanity might be able to pull together to survive. Unfortunately, nuclear winter is the fate of the rest of the planet, given the energy levels we are talking about here.

We can assume angle of incidence at 90 degrees to the surface, as that will deliver the most energy directly into the ground. We can assume the mass of the school bus to be roughly 10,000 kg (based on Median GVWR of school buses). The Magic School bus has shown to be indestructible (it's magic), so we can ignore the chances of it breaking up on re-entry.

So, we have a projectile massing 10,000 kg, and we want to slam it into the ground hard enough to destroy the Continental US. (I'm assuming we are ignoring Alaska and Hawaii, so we don't have to destroy an entire hemisphere.)

Our target is a spot 2 miles northwest of Lebanon, Kansas...the geographic center of the continental United States. Our blast has to be powerful enough to kill someone at around 2,000 km away, given the width of the US.

Of course, we have a bit of a problem. We don't have a lot of reference for the amount of splash damage caused by hypervelocity impacts. And, unfortunately, I'm having a hard time getting any impact simulators to properly model such high speeds (the best one died when I got too close to relativistic speeds). So, I had to get creative and try to figure out how much energy it would take to create the impact needed. This is the tool I ended up using to simulate the amount of energy delivered to the center of the US to get the desired effects. http://www.purdue.edu/impactearth/ It's built by Purdue University, so I give it a fair degree of credibility. The ultimate simulation I settled on in order to obliterate the occupants of an area the size of the US was a 15km impactor, at 72 km/s, with the density of iron. And calculated effects at 2,000km away.

The results are the ability to kill pretty much everyone with the thermal blast and air pressure wave from the impactor...and it will teach the people distant from the impact point quite a bit about how impacts work. So that their deaths may be educational.

The energy delivered by this impact is $4.48e^{9} MegaTons$ which is an order of magnitude greater than the impact which caused the Chicxulub crater. In order to show the lethality, lets look at what that tool says life would be like at the 2,000 km mark.

Impact. We see a flare of light that appears 25 times larger than the sun in less than a second.

I+7.38 seconds: Thermal Radiation peaks. If it is flammable, it ignites. Trees, grass, wooden buildings, clothing, hair, etc. Humans do not ignite, but instead suffer 3rd degree burns across most of the body. People inside solid non-flammable structures with thick walls are still somewhat safe.

I+6.67 minutes: The ground tremors arrive. At this range, they are pretty minor and only crack plaster...alarming, but not of note, given that the world is currently on fire.

I+12.7 minutes: Ejecta starts to rain down on the area...it's mostly dust. Again, the world is on fire, this is largely ignored.

I+1.68 hours: The pressure wave finally arrives. Winds gust up to 489m/s (1,090 mph). Air Pressure spikes to over four and a half times normal atmospheric pressure. The sound wave is part of this, at 113 DB. This blast is sufficiently powerful to obliterate 90 percent of all trees (turning them into projectiles), distort skyscrapers to the point of impending collapse, and simply flatten houses.

The time delay before the pressure blast arrives would allow that anyone who survived the initial damage may have wandered out of safety by the time the blast wave arrives (and hurls them at things at absurd speeds).

The only people who would survive this are those in underground bunkers.

So, that brings us to the next question. How fast to we have to toss a 10,000kg bus in order to deliver this much energy?

Convert MegaTon value to Joules

$$ 1 Megaton = 4.184*10^{15} $$ $$ 4.48*10^9 Megatons = 1.87*10^{25} Joules $$

Calculate based on Kinetic energy... $$ E=\frac{1}{2}*m*v^2 $$ $$ 1.87*10^{25} = \frac{1}{2}*10,000*v^2 $$ Solve for Velocity... $$ 68,454,948,688.9m/s $$ Well crap. That's higher than the speed of light. Which means we are getting into relativity instead of achieving that speed. Time to break out relativistic Kinetic Energy Equations. $$ E=\frac{mc^2}{\sqrt{(1−\frac{v^2}{c^2})}} $$ Plug in values $$ 1.87*10^{25}=\frac{10,000 * 299,792,458^2}{\sqrt{(1−\frac{v^2}{c^2})}} $$ And we solve for v. $$ \sqrt{(1−\frac{v^2}{c^2})} = .0000480618 $$ $$ 1−\frac{v^2}{c^2} = 2.3099*10^{-9} $$ $$ \frac{v}{c} = 0.9999999988450 $$ $$ v = 0.9999999988450c $$

So, there you have it. In order for a school bus to deliver $4.48*10^9 Megatons$ worth of energy, right at the heart of the nation, you need to be moving at $0.9999999988450c$

At this point, the magic school bus is basically a particle beam. But, as it is indestructible, it should manage such an impact no problem.

The long term ramifications of this impact are best defined as 'global extinction.' Miss Frizzle just slapped the reset button on Earth...most terrestrial life is history from the climate impacts this will have. Humanity may survive...but the outlook is certainly bleak.

NOTE: I am making some assumptions regarding Joules of Impact relative to level of destruction, I know. But I had to simplify this somewhere...

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  • $\begingroup$ Awesome answer! It is actually faster than I thought it would need to be, but then, it is a fairly small object and wiping out a continent takes a lot of energy. $\endgroup$ – bowlturner Aug 18 '15 at 19:05
  • $\begingroup$ What's the difference in speed between protons in the LHC and the Magic School bus? $\endgroup$ – Green Aug 18 '15 at 19:15
  • $\begingroup$ A quick google search says that the LHC can toss things at 0.999999991c $\endgroup$ – guildsbounty Aug 18 '15 at 19:29

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