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A bear fell from a height of $10$ metres from ground.
It reached ground in $\sqrt2$ seconds. But somehow, it didn’t get hurt.
What is the colour of the bear?

Note : There is no lateral-thinking tag.

Hint:

I solved this question a year ago, felt like sharing it. It can have another tag : 'geography'.

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    $\begingroup$ Probably something to do with polar bears. $\endgroup$ – Fimpellizieri Mar 13 '16 at 7:52
  • $\begingroup$ @Fimpellizieri Yes, probably... Please put it as an answer :-) $\endgroup$ – ABcDexter Mar 13 '16 at 7:55
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    $\begingroup$ This question is much more clear. $\endgroup$ – manshu Mar 13 '16 at 19:53
  • $\begingroup$ @manshu Yes, you are right. This question was on a coding/programming website, that's why it's not 100% correct. $\endgroup$ – ABcDexter Mar 14 '16 at 3:43
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    $\begingroup$ The answer is gold, right? $\endgroup$ – Joel Reyes Noche Mar 14 '16 at 7:27
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The bear is

White

Because

I haven't a clue, but every question that cares about the color of a bear refers to polar bears. Every single one. Won't anybody think about the brown bears or the black bears?! They want to be famous too!

Or, more reasonably...

Because for it to reach the ground in $\sqrt2$ seconds from free fall, it would need to be accelerating at 10 $m/s^2$ ($x = ½at^2$). Interestingly, acceleration on earth is a bit less than that. This is made worse by air resistance and many other unpleasant factors. But the bear is certainly closest to falling at that acceleration in the Arctic Ocean, which - conveniently enough - has polar bears. Not getting hurt when falling from such a height probably involves hitting "ground" that can give way significantly, thus decreasing the impulse at the end. I'd suggest a small iceberg.

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    $\begingroup$ Nitpick: an iceberg is not "ground"... $\endgroup$ – user17947 Mar 13 '16 at 9:10
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    $\begingroup$ Your calculation and mention of air resistance neatly rules out candy bears, which wouldn't get hurt, and also get short-shrifted in puzzles, but would fall measurably slower $\endgroup$ – humn Mar 13 '16 at 10:13
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    $\begingroup$ My favorite subversion of that trope is an answer to the classic: A hunter shoots a bear, walks 10km south, 10km east, and 10km north and sees the bear again. What color is it? Instead of the expected polar bear, my answer is actually: Brown (or black) and red. He shot the bear non-fatally, and it's been stalking him ever since. $\endgroup$ – Darrel Hoffman Mar 13 '16 at 17:59
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    $\begingroup$ @Darrel Are you aware that you can move the way you describe and arrive at the same spot from an infinite number of spots on earth? Cost me 100 dollars 10 years ago. $\endgroup$ – Peter A. Schneider Mar 13 '16 at 22:09
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    $\begingroup$ @PeterA.Schneider: Ah, but there are no bears near any of the other points. $\endgroup$ – Ilmari Karonen Mar 14 '16 at 2:35
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To fall at that rate it must either be on another planet, accelerated by something other than gravity, or be falling inside an evacuated chamber. The last of those seems the least unreasonable. But since it is unharmed by the vacuum, it must have been dead to begin with. And since it is unharmed by the landing, I think it must be a teddy bear, which could be any colour but is most typically brown.

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  • $\begingroup$ Good answer, but I have not used any lateral thinking tag. $\endgroup$ – ABcDexter Mar 14 '16 at 9:07
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    $\begingroup$ @ABcDexter, so? I haven't used any lateral thinking. This is the most direct reasoning possible from the stated constraints. $\endgroup$ – Peter Taylor Mar 14 '16 at 19:21
  • $\begingroup$ Yes, but you did overthink it. Your answer is logically correct but the question is not about the meticulous answer :-) $\endgroup$ – ABcDexter Mar 15 '16 at 5:19
  • $\begingroup$ @ABcDexter, have you ever timed a falling object with air resistance? When we did it at school, a small dense sphere falling about a metre took long enough that assuming constant acceleration gave about 6.5m/s^2. A large bear not in a vacuum and instinctively trying to slow itself down would take at least 2s to fall 10m. Getting your intended answer requires more over thinking than realising that the numbers must be way out. $\endgroup$ – Peter Taylor Mar 15 '16 at 5:50
  • $\begingroup$ Ye, I have. But if we include air drag in it, there is no way g would be 10 m/s^2. But again, the question was not meant to include any of the empirical factors. $\endgroup$ – ABcDexter Mar 15 '16 at 6:07
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The bear is

transparent, white, red, orange, yellow, green, purple, or black

because

it's a tardigrade, or "water bear". Tardigrades are notable for their hardiness, and would be the most likely of all creatures called "bears" to survive whatever conditions caused the force of gravity to be so strong, as well as the fall itself.
Note that the Wikipedia article doesn't mention the possible colours. I found them here.

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The bear is:

White.

Because:

Assuming these number are precise measurements, he couldn't have fallen $10$m in $\sqrt2$ seconds since that would mean he was falling faster and further than the laws of gravity permit (see Zerris' answer for the equation). So he must have fallen less than $10$m. In fact, he fell at most $9.807$m. And he wouldn't even have fallen that far if he was slowed down by any air resistance, scraping any parts of the tree, braking any branches or any farting. This could happen if there was a snow drift over the ground. That would also explain why he wasn't hurt. He hit the ground through a cushion of soft fluffy snow. So he's a white polar bear as expected.

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  • $\begingroup$ A really good answer. If there was option to mark two answers as correct, I'd have marked it also :-) $\endgroup$ – ABcDexter Mar 14 '16 at 9:23
  • $\begingroup$ ...or any farting. Per your suggestion, next time I find myself in freefall, I will try farting copiously to slow my descent. $\endgroup$ – feelinferrety Mar 15 '16 at 18:08
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    $\begingroup$ @feelinferrety Might save your life one day! $\endgroup$ – Paul Evans Mar 16 '16 at 0:51
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Ok, I will throw my hat in the ring. The trick to the problem, I believe, is

You wouldn't expect this much acceleration because of the effect of atmospheric drag.

Therefore,

The drop took place where drag is the least, at the top of one of the highest Himalayan peaks. The reduced drag more than makes up for the increased distance from the center of the Earth.

The bear was unhurt because,

it fell into the snow covering the mountain top.

So the colour of the bear

is really undetermined since, if you're going to load a bear into an aircraft that is basically a rocket and fly it up over the Himalayan mountains, you can pick any bear you want. However, I will say it was black and white since panda bears are indigenous to the area and because I happen to like panda bears and, yes, I know they are not true bears and that there are brown bears indigenous to the same area but I don't care. Black and white is my answer and I'm sticking to it.

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The bear is

BLACK

because

It's falling into deep snow hence it's a polar bear. Polar bears are black with transparent hair which makes them appear to be white. Of course, it could also be a common brown or black bear being dropped into a deep snowdrift - the presence of snow implies it is Winter, hence the bear would likely be hibernating.

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The colour is black, blue and various tinges of yellow, being the colour of bruises, though of course one won't see the colour because of the fur. Specifically, S=ut+1/2.at^^2 where a is the acceleration, normally about 9.81 m.s^^-2 at the earth's surface. Assuming zero initial speed, this simplifies to a=10/9.81 metres.s^^-2. which may be an approximation of 1, or if it is precise then the acceleration is rather greater than normal, which is marginally (not precisely) higher at the poles, partly because of distance from the gravitational centre (F=m1.m2/R^^2), and partly because gravity is minutely offset at lower latitudes due to centripetal force. So if the north pole, then obviously a polar bear with white fur.

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The bear's color is obviously

somewhere between silvery grey and chocolate brown,

because

the bear is a koala bear, and they come in a range of colors from silvery grey to chocolate brown;

and I know this because

1. The question mentions specifically that there is no lateral-thinking tag. However, it is rather odd to write such a thing. If indeed OP wanted us to solve the puzzle based on a straightforward use of logic, he/she would simply not have said anything about lateral thinking. Saying that there is no lateral-thinking tag can only be a trick meant to distract us from the reality that the puzzle should indeed be solved using lateral thinking.

2. Tellingly, OP used the British spellings for "colour" and "metre", as also used in Australia, home of the koala. The same spellings are also used in Canada, home to polar bears and other bear species, but that would be too obvious, and would not require any lateral thinking, which we are not supposed to use, and which we therefore (as I explained above) are in fact supposed to use.

3. Australia has a lot of sand. The koala could have fallen off a tree (which makes sense since it actually spends much of its life on trees, unlike other bears which normally do not have any business being 10 metres above the ground) and into a big pile of sand. That is why it was not hurt.

4. Other answers have mentioned all sorts of other bears. No one has mentioned koala bears yet. Clearly I'm on to something! My answer also involves the cutest kind of bear, possibly tied with Hugh Meyers' suggestion of a panda.

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  • $\begingroup$ Again, you are overthinking. And yes, I used british spellings because they still prevail in India. $\endgroup$ – ABcDexter Mar 15 '16 at 10:03
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Answer is

White.

From 2nd law of motion $ s= ut+ \frac{1}{2}a(t^2) $

where $s$ is distance, $u$ is initial velocity and $a$ is acceleration and t is the time.

Putting the values in the equation. initial velocity $u$ is 0.
$10 = \frac{1}{2} * a * 2$

that will result in a=10.

Here, for free falling acceleration $a$ is g (acceleration due to gravity).
so $g=10$.

As we know, acceleration due to gravity is slightly higher in poles as compared to equator(because Earth is oblate spheroid in shape).

So the location is poles and polar bears are white in color.

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