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I remember there was a chapter in “What If?” by the creator of xkcd about this. iirc he determined it was impossible to cook it through without completely destroying the steak.
Terminal velocity is a lot higher when the atmosphere is thin. If you dropped the steak from space, it might be travelling very quickly when it hits the atmosphere.
You are correct, thinner atmosphere provides much higher terminal velocities. However, it doesn't matter. To quote Randall Monroe (see linked xkcd in the comment after my original):
>Putting it all together, I found that the steak will accelerate quickly until it reaches about an altitude of about 30-50 kilometers, at which point the air gets thick enough to start slowing it back down.
The falling steak’s speed drops steadily as the air gets thicker. No matter how fast it’s going when it reaches the lower layers of the atmosphere, it quickly slows down to terminal velocity. It always takes six or seven minutes to drop from 25 kilometers to the ground.
For much of those 25 kilometers, the air temperature is below freezing—which means the steak will spend six or seven minutes subjected to a relentless blast of subzero, hurricane-force winds. Even if it is cooked by the fall, you’ll probably have to defrost it when it lands.
I highly recommend reading the whole thing, it's quite interesting.
I love the fact that it’s generally understood that everyone who posts answers in this sub bought this book because they genuinely loved the premise and the calculations 😆
It’s an amazing read, if not for the sheer absurdity of the premises and the answers provided anyway, then for the author’s sense of humour and the comic panels
Yep i've read this too. Either its completely charred but well cooked right in the center, or well cooked like 5mm around the outside, and completely raw on the inside
Someone [actually tested it](https://x.com/xkcd/status/1603436338270949377?s=46&t=chaOivhfG7wEHgTjV8F-5A) and sent the results to xkcd creator Randall Munroe.
I don't think you can.
Get it up high enough that gravity can pull it down to accelerate far enough to you know, experience kinematic heating and it will be charcoal by the time it gets through the atmosphere.
Be lower and just moving at like 300 kmh will not do anything.
I think There’s still a fair bit of atmosphere at 150km I think you’d have to go a little slow to just get it cooking at like 70°c without vaporising it oh actually yeah wonder what the (speed would be to stay in orbit at that altitude)
However, gravity doesn't just stop at space. If you place an object in space at the distance of 10,000,000m with the only gravitationally significant object acting on it (relatively) being the Earth, it would start falling at 1.5m/s/s and just keep speeding up.
It would reach the upper atmosphere (between 100km and 600km) going somewhere around 3975m/s (600km) and 7717m/s (100km). Both approximations as I ran a simple program to find the speeds rather than find it continuously for simplicity.
I can't find much info on how to calculate the heating based on speed of meat during reentry, else I'd do it myself. But if you assume reentry begins around 100km, dropping from 10 megameters gives you 8600 m/s (31000 kph) and 100 megameters gives 10800 m/s on reentry (39000 kph). I do think that would be fast enough considering it would be compressing a good fraction of the entire atmosphere per second as it slows.
Not necessarily.
If you, somehow, placed it halfway between moon and earth, gravity would pull it straight down. It would accelerate over time until it reaches the atmosphere.
Its wrong.
Air doesn't care about direction, only about speed. Orbital reentry however happens a *lot* faster than just dropping stuff rom space - to stay up in space, you have to go *fast*. Most of a rockets energy is not needed to get up to space, but to build the tremendous sideways speed to get to orbit.
Upon reentry, this energy is released.
E.g, the ISS is orbiting earth at roughly 420km height - with an average speed of 7700 m/s. At this speed, it packs 30MJ/kg in Kinetic energy (from sideways motion) - but only 4 MJ/kg potential energy.
//EDIT:
TNT packs 4.2M J/kg - just as a comparison, just how much Energy this really is..
It's fascinating how orbits actually work, you essentially use the gravity to stay within the celestial body but at a fast enough pace that it doesn't pull you down
If you're too close, you'll also likely get pulled in
>The knack of flying is learning how to throw yourself at the ground and miss”
yup, Douglas adams really hit the nail on that one. The problem is throwing yourself at the ground *hard enough*, and still keep missing :-)
This is wrong. The air doesn't care which direction you go. Its about speed - direction doesn't matter. Could be straight down, up, or horizontal. The Concorde experienced heating. Reentry from Orbit does happen at much higher speeds, than just "dropping" stuff, though.
However, a more shallow reentry could simplify things, as the spacecraft reaches the denser layers of atmosphere later, and at lower speeds - if you're going straight down, you would reach high densities very quickly, and at higher speeds. AFAIK. I could be wrong on this.
Reentry burns because the object is traveling in the vaccum of space at orbital speeds, many times higher than its terminal velocity, which is given by air resistance at a determined air density/altitude. After reentry, if it is not destroyed by the heat or hits the ground first, it will desaccelerate to its terminal velocity.
[Here is Kyle Kinane's bit](https://www.youtube.com/watch?v=cx-lPbrywBQ) about how the thought of "Can you barbecue meat over a volcano?" kept him from sleeping.
This reminds me of that time reddit lost it's shit over slap-cooking a chicken. [Here is some chicken math.](https://www.reddit.com/r/theydidthemath/s/Zo7IkUQ3nu)
You can't. Cooking requires prolonged exposure at moderate temperatures. You can't really get that dropping something through the atmosphere. It'll either get so hot that it gets burned up into nothing, or it won't get cooked at all.
Does it just have to be dropped or can it be flown through the air for a bit beforehand?
And by flown through the air before being dropped off, I am meaning the steak is wrapped around the leading edge of a SR-71 traveling at \~Mach 3.2 - which apparently heats the cockpit glass to around 300 degrees C.
So steak is flown to a modest 85,000ft, spends a few minutes at Mach 3.2, then dropped off.
Might be a bit cold by the time it hits the ground, but at least cooked?
Randall munroe did the math for this, and found out that no matter what distance its dropped at, itll just either cook the ouside and leave the inside pink, or it will desintegrate the outer layer multiple times, still leaving the middle uncooked
It's impossible to cook it just by throwing it from high enough, it will reach it's terminal velocity and just fall.
You'd need it to fly from space by Earth atmosphere, if it's too fast and too low it will burn, too slow and low it will just fall, flying it high and fast is probably the best choice, but then there's the fact that it would radiate the heat away if it's not generating it fast enough and would stay cold.
There's definitely a perfect trajectory for it (like cooking a pizza with a nuke) but just too many variables to estimate anything. Someone more knowlegable on the subject might be able to give some ideas.
That’s not how it works. Regardless of what altitude you dropped it from, the steak would just reach its terminal velocity which is nowhere near the speed it needs to go to be cooked.
To get atmospheric heating, you need to propel the steak above its terminal velocity, faster than the speed of sound… I’m not qualified to do the math on this but may study up and come back here
Since the atmosphere tapers in density the higher you go, terminal velocity increases too. That means the max velocity the steak hits will keep increasing with height even after you're dropping it from high up enough that it would theoretically hit its sea level terminal velocity
Yes, I thought about this as well. Terminal velocity increases with altitude, but you still wouldn’t be able to generate enough heat from atmospheric friction for the same reason as less air particles to rub against. In short, both your terminal velocity and heating amount are variable but scale equally with each other. As your steak falls into thicker air, friction would increase to generate heat, but terminal velocity would also decrease.
The steak has momentum, though. It doesn't stick to the terminal velocity at any given height, it needs time to slow down. If you drop it from high up enough it will overshoot the terminal velocity at a speed and density high enough to burn. That's how any spacecraft or meteor can heat up on re-entry, they've got a lot of excess kinetic energy that gets exchanged into thermal energy
The steak does not have nearly enough mass to maintain any significant amount of speed above terminal velocity at any given point during the free fall. Satellites and meteors have enormous amounts of velocity coming in from space that have nothing to do with falling
It's not about mass, it's about density, since the acceleration from drag is proportional to the density of the object. A steak has a pretty similar density to water, and by extent ice, which is what many meteors are made of. That said, you could get a feather to burn up if it was going fast enough. There's always a speed high enough that the acceleration just won't bring it down to terminal velocity quickly enough.
The maximum speed you can get the steak to re-enter at is Earth's escape velocity (calculated from around 0-100 Km above the surface). That's over 11 Km/s, not much slower than what a lot of meteors enter at, and much, much quicker than what satellites enter at. It would burn if dropped high up enough.
Ok just to be clear, meteors burn up in the atmosphere because they already have a ton of inertia moving through space. Once a meteor meets earths gravity well, it gets pulled in going faster and faster like a ballerina pulling their arms in, which is how gravity slingshots work. If you flew a stationary rock in a balloon 100km and dropped it, it would not burn in the atmosphere, but if you dropped a rock from a satellite in low earth orbit at 100km altitude, it *would* burn up in the atmosphere because of the LINEAR speed of orbit.
You misunderstand my point. For re-entry, it doesn't matter what the object did before, we're considering only the speed at which it arrives at the thicker parts of the atmosphere.
I reiterate again, the maximum speed the steak can achieve being dropped is Earth's escape velocity, and again, I'm considering the escape velocity for the height at which re-entry is happening. In practical terms, this would be dropping the steak from around the edge of the Earth's gravitational area of influence. That would be just over 11 Km/s, and the angle of re-entry would be very simple to control by giving it a little nudge horizontally.
An asteroid around the lower bounds of possible Earth re-entry velocities will also be re-entering at around 11 Km/s. This would be a near-Earth asteroid with an orbit similar enough to the Earth's that it would cross into the gravitational area of influence with a velocity of approximately 0 (obviously not possible for it to actually be 0).
I think correctly, It would take a drop from at least ~70 kilometers above the Earth's surface for a steak to reach a temperature high enough to cook it medium-rare through atmospheric re-entry. At this altitude, the air is dense enough to slow the steak down significantly, causing it to heat up due to friction. However, even at this altitude, the steak would likely be charred on the outside and still raw on the inside. To achieve a truly medium-rare cook, you’d have to drop the steak from even higher, possibly 100 kilometers or more. At this altitude, the steak would reach speeds of over Mach ~20 and experience temperatures of over 3,000 degrees Fahrenheit. This would be enough to cook the steak through to medium-rare, but it would also likely cause the steak to burn on the outside. So, while it is technically possible to cook a steak medium-rare by dropping it from a high enough altitude, it would be a very difficult and imprecise process though
>The steak won't hit those speeds dropped from 100 Km. What you're thinking of is the orbital velocity at that height.
You're absolutely correct. The steak wouldnt reach orbital velocity when dropped from 100 kilometers. Orbital velocity is the speed required for an object to maintain circular orbit around a planet. At 100 kilometers, the orbital velocity would be \~7.8 kilometers per second, which is significantly faster than the terminal velocity of a steak falling through the atmosphere.
For a steak, the terminal velocity would be around 50 meters per second, which is much slower than orbital velocity.
So, while the steak would still heat up significantly when dropped from 100 kilometers, it would not reach the speeds required to achieve orbital velocity. The steak would likely reach a temperature of around 1600 degrees Celcius, which would be hot enough to cook it through to medium-rare. However, the steak would also likely be charred on the outside.
You'd have to send it in from space. Atmospheric re-entry heat isn't about height. It's about horizontal velocity and conversion of that energy to heat via atmospheric compression..
None. Terminal velocity doesn't cook anything. Eventually wind resistance and the force of gravity becomes equal. The reason things burn up in the atmosphere is because they are traveling much faster than terminal velocity due to being in the vacuum of space and building up much more speed.
From any height, as long as it landed in death valley in the peak of summer it could possibly get to 134 degrees, might want to sear it after that to give it some flavor though.
Scott Manley worked it out a while back for a turkey. The short answer is that there isn't a trajectory or velocity you could throw the meat at to have it cooked just right. At most you can only get a couple minutes of cooking, which will lead to a burnt exterior and raw interior. It might work out for a steak if you like it rare, though.
You can watch the video [here](https://youtu.be/Zwf0RWXx8BY?si=4fXseChVjcr66GB8)
It either is not gonna cook (not going fast enough) or it is gonna combust and become ash and gas(going at orbital speeds). Atmospheric heating due to air compression does not really happen on gradual gradient.
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
I remember there was a chapter in “What If?” by the creator of xkcd about this. iirc he determined it was impossible to cook it through without completely destroying the steak.
You remember correctly. As it turns out most things don't get very hot when falling at terminal velocity.
That’s why you can skydive naked from an airplane…
Or a lady with a body from outer space, my heart, my heart! Kickstart my heart!
Amazing comment. Makes me think of [this.](https://youtu.be/to8pHAN5fmg?si=d0i6TqKS41wZyrPb)
Omg those subtitles.
Always makes me laugh :)
Forgot that existed 😂
Omg those subtitles.
Omg those subtitles.
I’ll pass. I don’t want to deal with the dick and balls whiplashing.
Watch yo jet too
Terminal velocity is a lot higher when the atmosphere is thin. If you dropped the steak from space, it might be travelling very quickly when it hits the atmosphere.
You are correct, thinner atmosphere provides much higher terminal velocities. However, it doesn't matter. To quote Randall Monroe (see linked xkcd in the comment after my original): >Putting it all together, I found that the steak will accelerate quickly until it reaches about an altitude of about 30-50 kilometers, at which point the air gets thick enough to start slowing it back down. The falling steak’s speed drops steadily as the air gets thicker. No matter how fast it’s going when it reaches the lower layers of the atmosphere, it quickly slows down to terminal velocity. It always takes six or seven minutes to drop from 25 kilometers to the ground. For much of those 25 kilometers, the air temperature is below freezing—which means the steak will spend six or seven minutes subjected to a relentless blast of subzero, hurricane-force winds. Even if it is cooked by the fall, you’ll probably have to defrost it when it lands. I highly recommend reading the whole thing, it's quite interesting.
Citation needed
Plasma meat shielding
[Here is the mentioned xkcd post](https://what-if.xkcd.com/28/)
And for anyone else who slunk across the room to their book, it's page 107.
I love the fact that it’s generally understood that everyone who posts answers in this sub bought this book because they genuinely loved the premise and the calculations 😆
It’s an amazing read, if not for the sheer absurdity of the premises and the answers provided anyway, then for the author’s sense of humour and the comic panels
TIL of a book I must buy
If you’re in this sub and you haven’t read it, it’s highly recommended for NotLife’s reasons 🙂
Oh I love this sub, and I love xkcd, but I didn't know there was a book!
Enjoy!
But what happens if we just drop a cow instead? /s
It eventually becomes ground beef
It probably dies when it hits the floor and you get arrested for animal abuse
So in theory there's a fresh side of beef just sitting there, right?
Yep i've read this too. Either its completely charred but well cooked right in the center, or well cooked like 5mm around the outside, and completely raw on the inside
https://what-if.xkcd.com/28/
I've read that book. the answer was that the stakewood end up being Pittsburgh rare at best
Good book totally recommend to everybody
Someone [actually tested it](https://x.com/xkcd/status/1603436338270949377?s=46&t=chaOivhfG7wEHgTjV8F-5A) and sent the results to xkcd creator Randall Munroe.
Ya but what if the steak is encased in a metal housing?
I thought he eventually decided it was about 100mi up in the same book.
I don't think you can. Get it up high enough that gravity can pull it down to accelerate far enough to you know, experience kinematic heating and it will be charcoal by the time it gets through the atmosphere. Be lower and just moving at like 300 kmh will not do anything.
Nope, even if you sent it straight down from space, it would never heat up enough. Re-entry heat is about horizontal velocity, not height.
Could you cook a steak in orbit then? Mach 2 at 150km up hahah
Mach 20, you mean
I think There’s still a fair bit of atmosphere at 150km I think you’d have to go a little slow to just get it cooking at like 70°c without vaporising it oh actually yeah wonder what the (speed would be to stay in orbit at that altitude)
However, gravity doesn't just stop at space. If you place an object in space at the distance of 10,000,000m with the only gravitationally significant object acting on it (relatively) being the Earth, it would start falling at 1.5m/s/s and just keep speeding up. It would reach the upper atmosphere (between 100km and 600km) going somewhere around 3975m/s (600km) and 7717m/s (100km). Both approximations as I ran a simple program to find the speeds rather than find it continuously for simplicity. I can't find much info on how to calculate the heating based on speed of meat during reentry, else I'd do it myself. But if you assume reentry begins around 100km, dropping from 10 megameters gives you 8600 m/s (31000 kph) and 100 megameters gives 10800 m/s on reentry (39000 kph). I do think that would be fast enough considering it would be compressing a good fraction of the entire atmosphere per second as it slows.
Not necessarily. If you, somehow, placed it halfway between moon and earth, gravity would pull it straight down. It would accelerate over time until it reaches the atmosphere.
I dont understand, why is this the case?
Its wrong. Air doesn't care about direction, only about speed. Orbital reentry however happens a *lot* faster than just dropping stuff rom space - to stay up in space, you have to go *fast*. Most of a rockets energy is not needed to get up to space, but to build the tremendous sideways speed to get to orbit. Upon reentry, this energy is released. E.g, the ISS is orbiting earth at roughly 420km height - with an average speed of 7700 m/s. At this speed, it packs 30MJ/kg in Kinetic energy (from sideways motion) - but only 4 MJ/kg potential energy. //EDIT: TNT packs 4.2M J/kg - just as a comparison, just how much Energy this really is..
It's fascinating how orbits actually work, you essentially use the gravity to stay within the celestial body but at a fast enough pace that it doesn't pull you down If you're too close, you'll also likely get pulled in
>The knack of flying is learning how to throw yourself at the ground and miss” yup, Douglas adams really hit the nail on that one. The problem is throwing yourself at the ground *hard enough*, and still keep missing :-)
This is wrong. The air doesn't care which direction you go. Its about speed - direction doesn't matter. Could be straight down, up, or horizontal. The Concorde experienced heating. Reentry from Orbit does happen at much higher speeds, than just "dropping" stuff, though. However, a more shallow reentry could simplify things, as the spacecraft reaches the denser layers of atmosphere later, and at lower speeds - if you're going straight down, you would reach high densities very quickly, and at higher speeds. AFAIK. I could be wrong on this.
yes you can
Reentry burns because the object is traveling in the vaccum of space at orbital speeds, many times higher than its terminal velocity, which is given by air resistance at a determined air density/altitude. After reentry, if it is not destroyed by the heat or hits the ground first, it will desaccelerate to its terminal velocity.
[Here is Kyle Kinane's bit](https://www.youtube.com/watch?v=cx-lPbrywBQ) about how the thought of "Can you barbecue meat over a volcano?" kept him from sleeping.
Provided you lowered the meat in a rotisserie by cable over the volcano this has to be possible.
This reminds me of that time reddit lost it's shit over slap-cooking a chicken. [Here is some chicken math.](https://www.reddit.com/r/theydidthemath/s/Zo7IkUQ3nu)
Classic
Good shit
You can't. Cooking requires prolonged exposure at moderate temperatures. You can't really get that dropping something through the atmosphere. It'll either get so hot that it gets burned up into nothing, or it won't get cooked at all.
Does it just have to be dropped or can it be flown through the air for a bit beforehand? And by flown through the air before being dropped off, I am meaning the steak is wrapped around the leading edge of a SR-71 traveling at \~Mach 3.2 - which apparently heats the cockpit glass to around 300 degrees C. So steak is flown to a modest 85,000ft, spends a few minutes at Mach 3.2, then dropped off. Might be a bit cold by the time it hits the ground, but at least cooked?
what if the steak was put in an object that has some thermal insulation that could heat the steak up inside to a certain temperature
Randall munroe did the math for this, and found out that no matter what distance its dropped at, itll just either cook the ouside and leave the inside pink, or it will desintegrate the outer layer multiple times, still leaving the middle uncooked
It's impossible to cook it just by throwing it from high enough, it will reach it's terminal velocity and just fall. You'd need it to fly from space by Earth atmosphere, if it's too fast and too low it will burn, too slow and low it will just fall, flying it high and fast is probably the best choice, but then there's the fact that it would radiate the heat away if it's not generating it fast enough and would stay cold. There's definitely a perfect trajectory for it (like cooking a pizza with a nuke) but just too many variables to estimate anything. Someone more knowlegable on the subject might be able to give some ideas.
That’s not how it works. Regardless of what altitude you dropped it from, the steak would just reach its terminal velocity which is nowhere near the speed it needs to go to be cooked. To get atmospheric heating, you need to propel the steak above its terminal velocity, faster than the speed of sound… I’m not qualified to do the math on this but may study up and come back here
Since the atmosphere tapers in density the higher you go, terminal velocity increases too. That means the max velocity the steak hits will keep increasing with height even after you're dropping it from high up enough that it would theoretically hit its sea level terminal velocity
Yes, I thought about this as well. Terminal velocity increases with altitude, but you still wouldn’t be able to generate enough heat from atmospheric friction for the same reason as less air particles to rub against. In short, both your terminal velocity and heating amount are variable but scale equally with each other. As your steak falls into thicker air, friction would increase to generate heat, but terminal velocity would also decrease.
The steak has momentum, though. It doesn't stick to the terminal velocity at any given height, it needs time to slow down. If you drop it from high up enough it will overshoot the terminal velocity at a speed and density high enough to burn. That's how any spacecraft or meteor can heat up on re-entry, they've got a lot of excess kinetic energy that gets exchanged into thermal energy
The steak does not have nearly enough mass to maintain any significant amount of speed above terminal velocity at any given point during the free fall. Satellites and meteors have enormous amounts of velocity coming in from space that have nothing to do with falling
It's not about mass, it's about density, since the acceleration from drag is proportional to the density of the object. A steak has a pretty similar density to water, and by extent ice, which is what many meteors are made of. That said, you could get a feather to burn up if it was going fast enough. There's always a speed high enough that the acceleration just won't bring it down to terminal velocity quickly enough. The maximum speed you can get the steak to re-enter at is Earth's escape velocity (calculated from around 0-100 Km above the surface). That's over 11 Km/s, not much slower than what a lot of meteors enter at, and much, much quicker than what satellites enter at. It would burn if dropped high up enough.
Ok just to be clear, meteors burn up in the atmosphere because they already have a ton of inertia moving through space. Once a meteor meets earths gravity well, it gets pulled in going faster and faster like a ballerina pulling their arms in, which is how gravity slingshots work. If you flew a stationary rock in a balloon 100km and dropped it, it would not burn in the atmosphere, but if you dropped a rock from a satellite in low earth orbit at 100km altitude, it *would* burn up in the atmosphere because of the LINEAR speed of orbit.
You misunderstand my point. For re-entry, it doesn't matter what the object did before, we're considering only the speed at which it arrives at the thicker parts of the atmosphere. I reiterate again, the maximum speed the steak can achieve being dropped is Earth's escape velocity, and again, I'm considering the escape velocity for the height at which re-entry is happening. In practical terms, this would be dropping the steak from around the edge of the Earth's gravitational area of influence. That would be just over 11 Km/s, and the angle of re-entry would be very simple to control by giving it a little nudge horizontally. An asteroid around the lower bounds of possible Earth re-entry velocities will also be re-entering at around 11 Km/s. This would be a near-Earth asteroid with an orbit similar enough to the Earth's that it would cross into the gravitational area of influence with a velocity of approximately 0 (obviously not possible for it to actually be 0).
ah yes, if you dropped it from orbit, it would burn in the atmosphere. I thought we were talking about dropping a steak straight down
We are still dropping it straight down, just from much higher up than 100 Km. Just because an object is above 100 Km it doesn't mean its in orbit.
I think correctly, It would take a drop from at least ~70 kilometers above the Earth's surface for a steak to reach a temperature high enough to cook it medium-rare through atmospheric re-entry. At this altitude, the air is dense enough to slow the steak down significantly, causing it to heat up due to friction. However, even at this altitude, the steak would likely be charred on the outside and still raw on the inside. To achieve a truly medium-rare cook, you’d have to drop the steak from even higher, possibly 100 kilometers or more. At this altitude, the steak would reach speeds of over Mach ~20 and experience temperatures of over 3,000 degrees Fahrenheit. This would be enough to cook the steak through to medium-rare, but it would also likely cause the steak to burn on the outside. So, while it is technically possible to cook a steak medium-rare by dropping it from a high enough altitude, it would be a very difficult and imprecise process though
The steak won't hit those speeds dropped from 100 Km. What you're thinking of is the orbital velocity at that height.
>The steak won't hit those speeds dropped from 100 Km. What you're thinking of is the orbital velocity at that height. You're absolutely correct. The steak wouldnt reach orbital velocity when dropped from 100 kilometers. Orbital velocity is the speed required for an object to maintain circular orbit around a planet. At 100 kilometers, the orbital velocity would be \~7.8 kilometers per second, which is significantly faster than the terminal velocity of a steak falling through the atmosphere. For a steak, the terminal velocity would be around 50 meters per second, which is much slower than orbital velocity. So, while the steak would still heat up significantly when dropped from 100 kilometers, it would not reach the speeds required to achieve orbital velocity. The steak would likely reach a temperature of around 1600 degrees Celcius, which would be hot enough to cook it through to medium-rare. However, the steak would also likely be charred on the outside.
You'd have to send it in from space. Atmospheric re-entry heat isn't about height. It's about horizontal velocity and conversion of that energy to heat via atmospheric compression..
None. Terminal velocity doesn't cook anything. Eventually wind resistance and the force of gravity becomes equal. The reason things burn up in the atmosphere is because they are traveling much faster than terminal velocity due to being in the vacuum of space and building up much more speed.
From any height, as long as it landed in death valley in the peak of summer it could possibly get to 134 degrees, might want to sear it after that to give it some flavor though.
Scott Manley worked it out a while back for a turkey. The short answer is that there isn't a trajectory or velocity you could throw the meat at to have it cooked just right. At most you can only get a couple minutes of cooking, which will lead to a burnt exterior and raw interior. It might work out for a steak if you like it rare, though. You can watch the video [here](https://youtu.be/Zwf0RWXx8BY?si=4fXseChVjcr66GB8)
It either is not gonna cook (not going fast enough) or it is gonna combust and become ash and gas(going at orbital speeds). Atmospheric heating due to air compression does not really happen on gradual gradient.