Although it's a grim question, I think we can come up with some approximate answers. Firstly, we need to know how easy it is to break bone. For this I had to turn to this research paper by Peter Fratzl on densities and breaking points of biological material. He points out that the angle of impact has an affect, but we're wanting to work out the minimum height required to guarantee bone breakage. In other words we want to take everything at it's least likely extreme. For this, Frantzl measured the impact as needing 9920 J/square meter in order to break a bone.
This tells us how much energy we need for every square meter of bone, so let's work out how much area of bone you've actually got. Unfortunately, nobody seems to have done any good research on this topic so we'll have to make a few estimates. According to Medicinenet.com the average human man has a surface area of 1.9 square meters. We'll use this number rather than the female number, since we're looking for the "most difficult for nature to pull it off" example. We also need to divide this number by two, since all 1.9 square meters don't hit the ground at the same time (you can't hit the water on the front and back of your body simultaneously) so we'll assume you hit the water in a perfect flop, giving you a surface area of 0.95 square meters.
This means the water is going to need to apply 9920 x 0.95 Joules of energy to the human body in order to make it break. That's 9424 Joules of energy needed to guarantee a bone break. What height would we need to achieve this kind of impact?
Energy done on the body can be calculated as mass x acceleration x distance. So we need the average mass of a human. According to Biomedicalcentral.com the average human has a mass of 62 kg. The average American is 80.7 kg, so let's go with that number. The distance travelled is referring to the distance you travel as you enter the water. This calculation gets extremely complicated because as height above the water changes, so does distance travelled into the water, so I'm going to use another back-of-the-envelope calculation and assume you come to a rest in about 2 meters below the surface. Energy = mass x acceleration x distance travelled. If this is a 9424 Joule change then we need an acceleration of 9424/161.4 (I'm just dividing energy over mass x distance here). This gives us a required deceleration of 58.4 meters per second squared.
Acceleration is calculated as (final velocity - initial velocity)/time taken to change. For this calculation, our final velocity is zero (because we've come to a rest) so we need to know how long it takes you to come to a halt once you hit the water. Calculating this is fiendishly difficult because we need to take into account the change in density from air to water, so I'm going to "back of an envelope" it once more and say it takes about 1 second to stop after you've hit the water. If you watch underwater footage of divers this usually seems about right. It also makes the calculation neater because now we can say that acceleration = (0-initial velocity)/1. In other words we can say that the speed you hit the water at is 58.4 m/s.
Now here comes the final step. What height do you have to be in order to hit the water at this speed? Well, fortunately for us, all objects accelerate toward the ground at the same rate, so there is a simple formula you can use to calculate final velocity. It's v = sq root (2 x gravitational acceleration x height). We know our final velocity is 58.4, we know gravitational acceleration on Earth is 9.81 meters per second squared which means if we do a simple rearrange we can calculate what height is needed: (velocity squared)/2xgravitational acceleration. In this case that becomes (58.4 squared)/2 x 9.81. This gives an answer of 173.8 meters.
So there you have it. If you want to be 99% sure your bones are going to break when you hit the surface of the water, you'd have to jump a distance of at least 173.8 meters. Now, a fall from a much smaller height could still break your bones if you hit the water at a certain angle, but 173.8 is what you'd need to guarantee it.
Hope you're happy now Vishal!
Density is a measure of how much mass you will find in a given volume. Nowadays we define it as the mass divided by the volume but, interestingly, 'twas not always so. In fact, Isaac Newton (the father of modern mechanics) considered density to be the more fundamental property and defined mass as simply the density multiplied by volume. Sam's question is a very good one: at what scale of the Universe do we start to notice density?
In the nucleus of an atom there are three main forces at work. The electromagnetic force causes protons to repel each other, while the strong force causes them to attract, along with neutrons. The weak force causes protons and neutrons to turn into each other and everything is held in a delicate balance. At this scale all three forces play an equally important role and the result is that all nuclei have the same basic layout.
All atomic nuclei have a fairly equal spacing of atoms meaning that there is an actual "nuclear density" common to all atoms. The value is around 2.3 x 10^17 kg for every cubic meter of nucleus you have.
The space between the nucleus and the electron orbitals also has a pretty consistent density because the distribution of mass is about the same for all atoms. We usually express this in terms of energy per volume rather than mass per volume (because the mass isn't stable) and it has a value of around 1 x 10^-9 Joules per cubic meter. That's quite a lot.
Where density starts to vary is above the atomic scale. Atoms are attracted to each other at a great distance but repelled by each other when they get too close. The sizes of these interactions depend on the size of the atom, the shape it has and how well shielded the nucleus is from the outer radius. Different types of atoms will therefore have different ways of squashing against each other. Ultimately this means different types of atoms will pack together differently and density as the real-world property emerges. So density differences are only relevant on the scale of atoms and bigger. Anything smaller and things are nicely balanced.
This is a really interesting question because I'm not sure how to answer it. Lichens aren't actually a single organism, they're actually a mixture of fungi and bacteria living off each other in what's called symbiosis.
Different types of lichen grow well in different environments. One particularly well known species of lichen (the technical name I can't remember) which is a sort of orangey colour tends to grow on the north side of trees in the northern hemisphere. The reason is because in the northern hemisphere the Sun doesn't rise and fall perfectly in the middle of the sky, it's actually tilted toward the South a little, meaning the south sides of trees get more sunlight. The opposite is true in the Southern hemisphere, the Northern sides of trees get extra sunlight.
The side which gets the most sunlight is usually not a good place for lichens to grow because they bake in the light and heat, so they tend to grow on the shaded side. So lichens can definitely be used to navigate.
Your question about the TV program and railways is more mysterious. I've never heard of lichens being used to map out railways, so here's a question posed to anyone reading: have you heard of this? Do you remember the same TV program Varena is talking about? I'd love to hear your responses in the comments!
Of the eight known planets in our solar system, every one of them is roughly spherical. The same is true for every sun and almost every moon. The reason is because the force of gravity acts in all directions.
Imagine taking a sheet of paper in your hand and scrunching it up really tight. You batter and squash from all directions which means it's getting squeezed from every side. If you do it evenly you'll end up with a ball-shape. Gravity works the same way, only inside-out.
Imagine that same piece of paper being squeezed, except rather than the force coming from outside and pushing in, the paper itself is collapsing into its own centre. It's being pulled in every direction toward the middle, giving us the same shape. For most everyday objects the force of gravity in their centre is so weak that it can't pull the object into a ball. A bookcase, for instance, has a gravity field pulling it inward toward a central point. The only reason it doesn't collapse into a bookcase-ball is that the bonds between the atoms in the bookcase are stronger than the pull of gravity. But on the scale of planets, things get a little different.
The more mass you have, the stronger the gravity field surrounding you. Planets are so massive that their gravity fields are able to pull them inward, wrapping them into neat, roundish balls. So that's why the suns, moons and planets of our Universe are all rounded. Everything has a gravity field to it, it points in all directions, and large objects collapse into their own fields.
Although in fact, most of the planets aren't perfectly round, they're more like squashed oranges. The reason is because the planets are spinning. As they spin, they spread out a little bit, causing them to bulge in the middle, which means the Earth is thicker near the equator than it is at the poles. In fact, if you let go of an object at the equator it will fall at a slightly different speed to the poles because there's more planet between them and the centre of gravity at the core.
The main answer is through the blood (circulatory system) and through various different types of neurons and nerves (nervous system). Human blood isn't just one chemical, it's actually hundreds of chemicals all being pumped along different channels. Oxygen, Carbon Dioxide, Blood cells, Hormones, Glucose and more are all carried from one cell to another in the blood, sort of like a highway in your body down which many types of vehicle can pass.
But a lot of the signals between different parts of the body are done via electrical signals sent along nerves and neurons. Your skin (arguably the largest organ in the body) is wired into your brain via the nervous system and can send it information about pleasure, pain, temperature and texture, all of which your brain processes, sending its own signals either down the nervous system or by triggering various glands (little chemical factories) which pump chemicals into your blood telling your body how to respond.
And these are just two two main systems. Your organs can also "talk to each other" indirectly by changing different parts of the body around them. Your muscles can produce acid which gets carried to the liver (mainly by the blood) and the liver responds by digesting it into less damaging chemicals, almost as if the organs have sent a message to the liver telling it to process the acid. Your body is really a network of different systems all communicating with each other whether you're aware of it or not. They do it in your sleep, when you're awake, when you're thinking about it and sometimes by accident.
We've all experienced the sensation of finally learning to do something after hours of failed practice. Somehow the brain seems to distinguish between successful and unsuccessful attempts. Aabha's question is a good one but the answer is very simple: nobody has even the remotest clue! What we do know is that memories are stored in different places around the brain and that when you reinforce a thought pattern, physical movement etc. your brain often becomes quite good at repeating it. But the brain is still flexible enough to allow you to try the skill (mental or physical) in different ways.
What's also interesting is that it doesn't happen instantly. When you learn to juggle, for instance, you don't suddenly find there's a moment when it clicks and you can juggle perfectly. You tend to find (I did at least) that once you start doing the juggle successfully, it still takes a couple of weeks of practice before you stop making the old mistakes. The same can be said of learning a fact in school, often it takes reinforcement before we stop making the previous mistakes.
Although, some types of information do seem to be like flipping a switch. If someone has always thought Mars was the colour green, it takes 30 seconds for them to learn it's red and they never make the mistake again.
All we can really say is that the brain has the ability to repeat its' activities, vary them, self-analyse, self-observe and compare actions with an internal set of "success criteria". Sometimes it can take a long time for the brain to learn the correct pattern, sometimes it can be instantaneous. Sometimes the brain rewards you for a new way of thinking, sometimes it punishes you (like when you lose sleep over a new frightening statistic you've learnt).
As a teacher, I wish I knew the secret to helping people learn something. If I knew (or if anyone knew) what was going on inside the brain when we learn a new skill, fact, way of thinking...I'd have discovered the silver bullet of education. Sadly our knowledge of the brain is nowhere near good enough to answer the question even a little bit. All I can say is that your brain can somehow distinguish correct from incorrect IF both options are made explicit i.e. you only know you've got it wrong if you know what right looks like.
A mirror is obviously a surface which absorbs very little of the light hitting it and bounces it back in all directions. So, by any reasonable definition, a mirror is white. But it doesn't look the same as normal white objects obviously. The reason for this is that there are actually two ways a surface can reflect light: Specular reflection and scattered reflection.
In specular reflection, every beam of light is bounced back perfectly at the same angle it came in. If a beam of light hits a surface at 60 degrees, it bounces out at sixty degrees. This is sort of "perfect" reflection and this is what's happening when we look at a mirror. In scattered reflection, the surface of the object isn't as smooth, so the beams of light do get reflected back at their original angle, but they get scattered in lots of different directions because the surface is jagged. This means we get all the beams of light coming out, but they are mixing with each other, crossing over and the original "image" is lost. This is what a white object is doing.
So a mirror is, in one sense, a perfectly smooth white surface, while a white object is a rough or jagged white surface (compared to the mirror of course). Perhaps we might want to say that a mirror is "mirror coloured" to describe "white specular".
A percentage is another word for a fraction. A fraction of 100 specifically. So to express 0 as a percentage of 0 we're asking the question: what is 0 divided by 0? This is an interesting question because there are four possible ways to answer it. In one sense we are taking an even number and dividing it by itself, making the answer 1 (100%). In another sense we are taking a zeroth of something, making the answer 0 (0%). In another sense, to divide by zero has an undefined solution, it's a quirk of mathematics that doesn't actually mean anything. Like if I said the words: Three plums diefy. That sentence follows all the grammatical rules of the English language and makes internally consistent sense. But it doesn't actually relate to anything in reality. Likewise 0/0 follows all the accepted grammatical rules of mathematics, but relates to nothing, so the answer is indefinable.
There is another fourth answer which Scientists tend to use. We tend to think of division by zero as being equal to an infinite solution. To put it crudely: dividing by 0 = infinity. There are definite examples where this can be shown to be the case, any inversely squared distance law gives the answer of infinity when dividing by zero, so Scientists think of it like that. However, Scientists also treat this as evidence that our hypothesis is wrong. If you divide by zero and generate an infinity, you've got something which can't be described in terms of the actual world, since nothing is truly infinite.
The best answer to the question is really to say that the question is grammatically sound but semantically meaningless. It doesn't actually make sense as a question and is, as such, unanswerable.
Travelling into the future is completely possible due to the effects of special relativity. If you move through space very fast, time will slow down for you compared to the rest of the Universe. You will only have travelled for a few minutes, but everyone else might have aged by several decades. So travelling to the future is definitely a real thing and astronauts do it all the time (on a small scale). As for travelling to the past, then it gets a little bit fuzzy.
The best answer is really to say nobody knows yet. There are some experiments in quantum mechanics such as the delayed choice quantum eraser experiment which do give the impression (possible illusion) of events in the present affecting choices in the past but it's very hard to confirm that this really is what's happening. In quantum field theory the notion of CPT conversation shows that time-reversal is allowed mathematically, and in fact may be happening at the particle level all the time, but this is again only an interpretation of experimental data and what's going on may be something else entirely.
At the end of the movie Gravity, Sandra Bullock's character manages to pilot and crash a module into an ocean, surviving the impact and making it to the planet surface. Oli's original question is: which planet is she landing on? The answer is definitely the Earth, for two reasons.
Firstly, the rest of the film takes place in orbit around Earth and to crash onto another planet would be too enormous a distance to travel. The distance between the International Space Station and Earth, compared to the distance to the International Space Station and Mars (the nearest planet) is like the distance between your left eye and your right eye, compared to the distance between your left eye and Antarctica.
The second reason we can decide it's Earth is that there are lots of plants around. At the moment, Earth is the only known planet in our solar system to have plants. If she'd landed on Mars it would have looked like a rough, reddish brown desert. Not a fun place to be. So the answer is definitely: she's crash-landing on Earth.