Riddle : How many coins do you need to measure height of Burj Khalifa || Think out of the box
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- Опубликовано: 12 сен 2024
- Logic riddle interview : How many coins would you need to measure the height of the Burj Khalifa Tower?
Based on my own experience... only 10% of the people can answer it correctly. And the remaining 90% answers would be very funny and innovative.
So, even if you solve the problem correctly, I would highly encourage you all to comment below with a unique funny answer so that we all can enjoy the funny yet innovative ideas.
But you must think logically for the real solution.
Stacking up coins in any way or flipping is neither a practical solution nor a logical solution. So we have to think out of the box to figure out a logical approach.
You can share puzzles and riddles with me on these links:
Gmail : logicreloaded@gmail.com
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Air Resistance left the chat.
Time taken by sound to reach there never entered the chat
@@satyamlalchandani20 will it even reach there lol
we also have to consider bouyancy for such heights
@@satyamlalchandani20 don't trynna be oversmart man
Negligible
Actually the answer is no coins, as you enter the lift it tells you the exact height on a poster.
@Garv Jain yes we can use trigonometry but you must answer as per the Q
The importance is not the height of Burj in the riddle , its how u can measure it using a coin
I think you'd need quite some coin, just to get past the welcome desk.
@@anandunambiar1032 You can use trigonometry and simple aritmethics, just step somehwere out of Burj move a coin till it covers from top to base of the buiding, the height of the building is the coin diameter multipled by the number of times the distance of the eye to the coin is cover from the observer to the tower base. The outcome will be no less precise that time as there is something called "air" that makes the results not too precise
The elevator is a box, you're only allowed to think outside of it.
I tried your solution with my friend, I dropped the coin and my friend is still searching for it until this day
awesome comment bro😂😂😂
😂😂🙏😂😂
Haha
How good a friend? Did you check her/his pockets?
You didn’t throw it far enough and it caught on one of the intermediate level roofs. Oh well.
One coin. Stand at a distance from the base of the Tower in clear sight. Keep coin horizontally at breast height and try to cover the building with the coin (diameter). Measure the distance from the base of the tower and then it's just similar triangles.
how will you calculate base length?
Measure base length with car's odometer!
@@manishtanti8432 GPS
@@manishtanti8432 Laser distance measure will be even more accurate
How can we keep the coin horizontal and cover the building??
Hey!
I have a different approach:
1) walk far away of the tower, take one coin, and place it in front of your eye so that it matches the height of the tower.
2) measure the distance between your eye and the coin.
3) measure the distance between you and the tower.
4) measure the height of the coin
5) you can then solve for the height of the tower as we have here similar triangles, or using Thalès theorem.
You beat me to it. I just commented the same thing before I saw yours.
Instead of using eye, a smartphone with single camera will give more accurate result.
Assuming the eye works like a pinhole camera, you might need two coins to figure out where the "center" of your eye is for steps 2 and 3. And if we can use a camera, that would make measuring a lot more reasonable i think
Creator uses a physics equation to calculate the height but entirely forgets about air resistance and terminal velocity.
Yes. The creator's riddles are often pretty dumb. In this case, you also need a watch. At which point the coin is useless. Just write the launch time on the watch and toss it to your buddy on the ground. At which point it's not you measuring the height of the tower. So much dumb! Just measure the length of the shadow at the moment your own shadow is exactly the same height as you are.
My solution is to hold the coin far enough away from your eye so it obscures the entire tower. The height of the tower should be (size of coin)x(distance from eye to tower)/(distance from eye to coin). You can use either eye but a larger coin is recommended or you'll have to have it really close.
@@crowbar_the_rogue That’s exactly the solution I came up with and is definitely better than the one in the video.
Or the wind which flows down from any high building accelerating the fall speed.
@@crowbar_the_rogue This was my initial thought as well
For the case of dropping the coin, the building is tall enough that the coin would reach it's terminal velocity. This can be mitigated by dropping the coin from a known height large enough to reach terminal velocity and then using that to calculate the terminal velocity.
Another option is to stand back far enough that the tower appears to be the exact height of the coin when you hold it out in front of you. Then using trig and the known values of distance to tower, eye height, arm length, and coin diameter you can calculate the height of the tower
Stacking or flipping coins is impractical but dropping a coin from the top of Burj Khalifa is 100% practical.
Good job.
Exactly my thoughts as well 😂
and what about air resistance... top of this building air speed can make humans blow away
The idea of a friend spotting the falling coin and being able to accurately stop the clock is silly, and the possibility of the coin being affected by the elements too.
@@jessicataylor7174 you don't have to see the coin, you just have to hear it,
So practically you can stand on the top of this tower and drop a coin from that point, love to see that.
We need 1coin to drop and a lot of money 💰 to go top of Burj tower 🗼😂
True 😂
Absolutely right :)
We need many coins
Can't drop a coin from the top of Burj
It will bounce off the many non plumb levels, most possibly stopping along the way. We need to also spend for installing a crane or scaffolding, or possibly rent a helicopter and use a lazer level to sight to the top of the building when starting the drop. Totally less practical than most any other method presentable, if they are eliminated for the sake of "practicality so we must use the timing method."
One coin, with a completely different approach.
Put the coin, of diameter d, on the ground, standing on its side. Measure the length l of the shadow of the coin.
At the same moment, measure the length s of the shadow of Burj Khalifa.
Then the height h of the Burj Khalifa satisfies the formula s/h = l/d.
Hey I really like this approach! Its actually more reliable and involves no factors like air resistance and terminal velocity like the dropped coin, kind of wish I had thought of this one!
One coin: Weigh it at the top and on the ground. The difference gives the height. Free fall is NOT under the only influence of gravity, but also air resistance.
that's an extremely cool answer
You can use 0 coins if it's a sunny day. Go out, measure a ratio of your height to your shadow length, then measure burge hallifa's shadow, and multiply it by your ratio.
(measure a ratio of your height to your shadow)? With what. If you were allowed to use a measuring stick in this puzzle. Then go full on and use a tape measure from the top to the bottom. We could use your idea, and it is nice. But we need at least one coin. We could measure the shadows with the coin. Or we could grab some random object and express our answer in terms of it. Who said meters and inches had to be used?
@@vangildermichael1767 Dropping the coin requires you to use a stopwatch. There's nothing in this puzzle that states you cannot use a tape measure.
The nice thing about this technique is that it would actually WORK. So would looking up the height or a dozen other techniques - dropping a coin (as described) wouldn't work.
1 coin
Hold one coin close to our eye and and when we see the both coin and building's length as same , then rotate the coin 90° and mark the spot of other end. Then using a tape or something take the distance reading.
Length will be exact same as of the building.
Or, you can do some fancy math with triangles and get the actual height!
@@AyrtonTwigg Can You Please Explain The Steps?
One coin, but a valuable enough one (such as gold) that you can hold it up and say to someone "you can have this coin if you go and find out for me the height of this tower".
I had the same idea. But in that case just do a bank transfer and you'll need 0 coins
Phone the architect of the building and ask him.
Actually i feel this approach is wrong, the wind resistance will be different just in case the coin rotates.. also its impossible to drop the coin from that point .. you will have to throw it from the top, which will result in a projectile motion at the start.. 😊
Why not trigonometry.?
@@RAKESHPAWAR27 what's your approach on the basis of trigonometry?
@@omprakashsonteke8033 one can use rules and the sunlight (and the shadow). Total number of coins required: 0.
On technicality one could hypothetically toss a coin such that its motion is 0 mph at the peak of the building.
@@RAKESHPAWAR27 The earth isn't flat.
Walk away to a known distance where when you lay on the floor and place the coin in front of you it will be as big as the tower then you can use similar triangle formula to calculate the height.
the distance between your eyes and the coin divided by the height of the coin equals the distance from your eyes to the tower divided by the height of the tower.🙂🙂
Underated comment
I was considering spending some coins for a more suited measuring device.
Stuff it, use one coin to buy a tour guide or just google it for free and keep your money! 😁
If you increase the speed Air Resistance will be rises according to the square of the speed. So you are gonna get a worse result.
Get enough of them to hire a physics professor or just go all in and bribe the guy that made the question lol
1. See the building from far distance and compare it's height with coin. The coin and building have same height(Adjust it to coin height)
2. You need no coin - apply Pythagoras theorem(measure distance from building outside and hypotenuse)
we can do without any coins just by measuring your height, shadow length and using a shadow length of tower,assuming it's a sunny day.
Same method I thought..... the ratio of hight and Shadow will be same
You do know that earth is round, correct ?
@@cool-aquarian we can assume circle's arc as plane if the arc length is too small with respect to the radius.
This uncertainty will remain forever.....u can't go beyond plank' lenth
Well the thing I didn't expect was the formula, and the thing I didn't know was the height of the tower. It's simple but needed critical thinking. Anyway good video, keep up the good work sir. :D
Appreciated the feedback :)
@LOGICALLY YOURS My physics textbook formula. Ur killin me.
Gift wrap 200 coins, visit the guy who designed the building, ask him to accept the gift and kindly tell the height of the building.
lol.
wallah aur coins mangti
One.
I. Offer a Krügerrand to the architect and ask.
II. Turn the Krügerrand into a wire (a Krügerrand will give you up to 100 km of gold wire, IIRC)
III. Put the Krügerrand on the ground and (quickly) take a photo from the top to determine the angular size.
IV. Ask Niels Bohr for futher options
Dropping it will not work because the coin will reach terminal velocity after about 100m of fall.
Yes, we always calculate those things in class assuming frictionless vacuum, but I always make clear these numbers are wrong and only approximations, but integrals are still two years away in math classes.
One coin: you measure the distance between the coin and the building at the moment the coin is the same size to the building. Angle, height, distance and coin size.
Thought the same!!😉
If you can measure the distance, then the coin is pointless.
@@siddharthsingh1994 please don’t try to walk vertically, my friend...
At some time during the day, the Sun will cast a shadow where the length along the ground equals the height. Use one coin to find what time this occurs, then find the tip of the tower shadow, and measure the distance to the base.
As much as the person with measuring tape wants as a rent.
I don't know if I'm glad or upset that I read the comments before providing a funny response of my own, since this was pretty much the same idea that I had.
@@RemyWillard Glad that we're in sync!
this is similar to the question how would you measure the height of a building with a barometer to which the innovative answers were:
a) go to the caretaker and say if you tell me the height of the building I'll give you a barometer
b) tie the barometer to the end of a piece of string. hang it off the top of the building, then measure the length of string.
c) place the barometer on the ground a suitable distance from the building that it appears to be the same height then by similar triangles for the distances to the barometer and building deduce the height from the scaled barometer height.
d) throw the barometer off the top & use your s=ut+0.5at^2
e) using 26feet/mBar is just boring
In answer to the original question the number of coins needed is zero... you can get a measure of the height from google. You can measure the height with a ruler. You don't need any coins at all to measure the height
Was thinking placing a standing coin far enough to cover the whole building, use distance and height of a coin by solving a congruent triangle problem, this might more practical than climbing to the tower
But being perfect would be extremely difficult over such a large distance.
The earth isn't flat.
It depends the distance of collision point you take, else you can use the coin to measure the elevation angle between the shade of tower to its top
Before watching for the solution, this is my answer: You need one coin. Drop the coin from the top, time how long it takes to hit the ground, apply the acceleration due to gravity formula, and you get the height.
Alternate answer: 50. Take a stack of 50 coins, it doesn't matter what denomination. On a sunny day at a given time, put the stack of coins in a sunny location where it will cast a shadow. Measure the height of the coin stack and the length of the shadow. This gives you two legs of a right triangle; use the Pythagorean theorem and some trigonometry to find the third side and the angles. From here there are any number of ways of using algebra, basic geometry, or trigonometry to find the height.
The simplest one would be this: Measure the length of the shadow cast by the building at the same time as the shadow cast by the coin stack. This will give you the ratio of the lengths of the two shadows. Take that factor and multiply it by the height of the coin stack. This will give you the height of the building.
Alternate answer three: One coin. Use a high value coin, like a British 5 pound coin or a 5 euro. Go up to the doorman, and offer him the coin as a tip in exchange for telling you the height of the building.
What about Air Resistance?😂
You yourself find the answer
As you raised the question now you can create your own answer
Its a good question
@@gowthamsaladi4960 we will drop the coin and measure the time taken by the sound to reach the top
@@pryo2460 From the top you can't hear people at the bottom shouting but you expect to hear the clink of a coin hitting the ground? :D
@@jessicataylor7174 not with naked ears...with some wave catching devices
@@pryo2460 This is a good plan, then for that we have to create a mechanism by which a detector will receive the sound at the top and in that case we won't need to drop a coin, we could make a noise at the bottom loud enough to reach the height.... The plan is good... But doing it using Trigonometry would be far easier and practical and that would have more accuracy too...😂 LoL (0 coins required)
If you have to measure it with a coin, it would probably be much easier to measure it using perspective. Travel a measured distance from the building such that when you hold the coin at a fixed distance from your eye it is seen as the same height as the building. Use the ratio of distance from your eye to the coin and distance from the building to your location and apply that to the height of the coin to determine the building's height.
I think a simpler solution would be the basic math example where we calculate height based on shadows. You can use basic geometry on right hand triangles along with the Pythagorean theorem.
Abe gadhe coins se krna h to fir..hadd hoti h
and for that, how will you measure angle of elevation? how will you measure the hypotenuse that is slanted distance between tip of burj khalifa and your eye contact point? you may be able to measure length of shadow, but based on the known value of only shadows measurement or base, how will you find height of burj khalifa without knowing angle of elevation and hypotenuse?
How are you editing all these things??? Which app r u using?
Required coins will be the no of coins which you need to pay for going to burj khalifa from your place for measuring it's height 😂😂
:)
lol
One (or two) coin(s) on a clear day. follow the tip of the shadow of the building until the point of the day when the coin stood perpendicular casts a shadow one coin length away. (If this is deemed impractical due to the movement of the coin, use two.)
Starting at the tip of the building's shadow at that moment, flip the coin directly toward the building, taking care to offset the thickness of the edge on each flip. (If this is deemed impractical, use a second coin to move between the two, counting the number of times you lace each. This method also assists in keeping the line direction exactly to the building.)
If you can assume an arbitrary time "for the sake of the riddle", then you can also assume, for the same sake, the ground from the shadow tip to the building is flat, and no obstacles are in the way.
I thought of using trigonometry and concept of height and distances. Here we use shafow of burj khalifa and shadow of coin in which ratio of sides should be proportional so that we can find the height of burj khalifa..😂
By this method here also we want one coin 😂
If wrong please comment👍🏾👍🏾😀
My solution as well.
You will need 1 coin standing on the edge a known distance away from Burj Khalifa on a table with a known height, you know the diameter of the coin. Now you measure the distance from the coin where the angle is such that you just see the top of the tower seen from the base level of the coin on the edge over the top level of the coin. Now, measure the distance to the coin and you should get 2 sides of a right triangle: Adjacent, the distance to the coin and opposition, the hight of the coin. Using the formula Opposition/Ajacent = Tangent θ(use the tangent- ¹ deg in your calculator). Knowing the angel and the distance to the tower you can repeat the calculation Tangent θ( tangent deg in calculator) X Adjacent = Opposition, which is the height of the tower - the height of the table on which the coin was standing, so adding the height of the table to the found opposition will get you the true height of the tower.
You must be a superhero to throw coin just vertically from that top...😂😂
yeah and the second dude standing at the exact spot where the coin lands
1) Find the person who owns the building and say "If you tell me the height I will give you this coin."
2) Drill a hole in the coin. Tie a string to the coin. Dangle it off the building until it touches the ground. Measure the string.
3) On a sunny day measure the length of the building's shadow. Then stand the coin on edge on the ground and measure it's shadow and diameter. Using the ratios of similar triangles compute the height of the building.
4) No coin. Stand far enough away to see the top of the building. Use a laser rangefinder to measure the distance to the base, and then to the top. Compute the other leg of the right triangle.
By applying trigonometry 😂😂
I think this has to be a troll
You can hold a coin far enough back where if you hold the coin in front of the building it covers the whole building. Measure the angle that it makes and calculate using similar triangles.
When the teacher tells u air resistance can be neglected
1. Stand one coin on its edge.
2. Measure the length of the coin's shadow.
3. Divide the length of the shadow with the diameter of the coin to get the value X.
4. Measure the length of Burj Khalifa's shadow.
5. Add to this length half the diameter of Burj Khalifa to get Y. (Approx. To account for the distance of the tip's horizontal distance from the edge of the building at base.)
6. Y/X is the approximate height.
7. You should also account for the unevenness of the ground surface and the curvature of the earth. And the two measurements have to happen at the same time so the sun is at the same position.
Another solution:
1. Get a camera to point at Burj Khalifa.
2. Set the coin up in front of the camera so that the coin is parallel to the lens and it's just covering the view of Burj Khalifa.
3. Measure the distance between the camera's focal point and the coin to get value X.
4. Measure the distance between the camera's focal point and Burj Khalifa to get Y.
5. Burj Khalifa's height is approx dX/Y, where d is the diameter of the coin.
RIP surveying instruments
Stand the coin vertically on edge, measure the shadow and coin.
Measure the shadow of the Burj Khalifa.
They are both similar right triangles, so the height is equally proportionate to the shadow.
Dropping the coin doesn't work unless you know the terminal velocity of the coin as the coin will CERTAINLY reach terminal velocity in under 1 second, as DRAG is a SECOND FORCE on the coin.
This episode is *Unphysically Yours* !
Come on! Air resitance, terminal velocity, wind velocity. And also the fact that you cannot get to the *very top* of the building to drop the coin.
How about I give a coin to some guy to get the answer from the building's blue print or some official document? 🤣🤣🤣
What a funny reply! All your funny replies make me laugh. The *correct* answer is that it's a high school physics problem for some reason.
@@jamesdavis3851
"High school"? Which one? Because the definition of "high school" is different from country to country or even within US. I would think you're talking about "senior high school".
Well, I don't know in which (senior) high school or in which country where students are NOT taught about terminal velocity ....
I would rather say it's a *junior* high school problem.
@@Horinius It varies, but I've taught physics at around 9 universities and we don't do much with terminal velocity except that it exists... it would be a terrible problem at any level, but I could imagine a terrible teacher assigning it
@@jamesdavis3851
Being a master degree physicist, I totally understand that terminal velocity formula is not usually taught or used. Moreover, we are dealing with a coin, not a ball. So, there's no easy model for it.
But it's "OK" that the terminal velocity formula is not used because what's important is that students should know that the free body equation is ONLY valid for low altitude, like a few tens of metres. Most certainly for not hundreds of metres LOL
Yes, this problem is terrible. It's very unphysical as I've written at the very beginning of my comment. Cheers.
@@Horinius Yeah, totally. My original comment was just meant to be sarcastic and mocking toward the presenter, who made a ridiculous model, labeled it as "CORRECT", and said he was looking forward to everyone else's silly ideas.
Edit: And sorry, I didn't check that you made that comment 2 years ago, so I shouldn't have expected you to remember the wording that the guy used in the video to pick up on the sarcasm lol
If we know the height of the building
(say 490m)
Then we can take the measurement of no. of coins in 1m (say 20 coins)
Then we can multiply 20 coins and 490m to get actual no of coins needed.
it's over 800 m dude
It needs only one coin to solve the puzzle but for making it practically it takes coins equal to my one year salary. So it takes more than one coin brother
What I would do uses these formulas:
v^2 - u^2 = 2as
v = u + at
s = vt - 0.5at^2 = ut + 0.5at^2
s = 0.5t(u+v)
s= distance (height of BK)
u= initial velocity (here 0)
v= final velocity
a= gravitational force
t= time of flight
Finally, s= 0.5gt^2. Plug in time of flight, and s= height.
One coin of the value equals to the price of a measuring tape😀
Or a theodolite, or something else. If the riddle allows a stopwatch, why not use something that gives you the exact height?
@@johnlister yes you are right but the idea of theodolite is not so worthy as it can measure only angles on vertical and horizontal axis.......
It will not give us soo much accuracy....
Okay I have an idea of using modern hypsometer as it will measure height as well as it's angles too
Hypsometer consists clinometer and laser laser rangefinder....
@@suryanarayanmishra5254 Sounds about right. And will work, no matter what the wind’s doing!
You also need to know the terminal velocity and drag of the coin, you cannot just use s=1/2at^2. It's impractical to get a long vacuum tube.
That falling coin can potentially kill my friend, who is on ground to stop the timer and I'll never risk my friend's life.
Your friend is safe. The terminal velocity of coins is not enough to kill, just enough to slightly injure. Your friend might get a coin shaped bruise.
@@josephcote6120 true. They busted that myth in mythbusters. But that was empire state and this is Burj. I know, I know... Just a joke!!
Your friend doesn't need to catch the coin. When the coin hits the ground, stop the timer. We don't care about the coin (if it breaks or not).
A superior method is to measure your distance from the tower , hold a coin, (or clustered row of coins of precise length) up to your line of sight, until it blocks your vertical view of the tower. Then high-school trigonometry solves both triangles. This may be more or less accurate depending on your elementary surveying skills. But anyone can do it within a reasonable radius of distance from the tower.
Your fictional thought experiment is highly impractical considering the likely-hood of actually getting to the actual top of the tower, wind resistance preventing the coin reaching velocity, or colliding with building that seems to be wider at the base etc.
Terminal velocity be like - You forgot me :(
Pigeon be like, "ouch!"...
Practical? First, you would have to be able to go on top of the roof and climb the spire.
Second, if you drop a coin it would land on the roof. Because the building gets bigger at the bottom you would have to bring along a pole to extend the coin out beyond the base, probably 50 meters. (It would weigh hundreds of pounds, to be strong enough to support its own weight.)
Third coins of different sizes have varying wind resistance. And I assume that at that height it would reach terminal velocity at some point. And your friend would have to be able to react with hundredth of a second timing.
Solution: Now mind you, I'm a high school educated carpenter.
It requires one person and one coin.
Stand a known distance away from the building hold a coin away from your eye till it just covers the building. Measure the distance between your eye and the coin. Find the hypotenuse of the triangle made by the height of the coin and length to eye. (Asq + Bsq = Csq) . Extrapolate by the distance from the building.
If your measurements are very accurate you should get a true height of the building verifiable by multiple distances.
Dropping the coin from the top would be "highly impractical" and an estimate at best.
Wow, can't believe i chanced upon this once it's uploaded. thanks for sharing!
Try similar triangle approach.
< I wish I could upload a picture to describe the answer. >
1. set yourself in an enough (known) distance (lets call D) away from the tower.
2. Now, move the (one) coin (lets call diameter of the coin as h) away from your eye such that the coin exactly obscures the tower.
3. Measure the distance between your eye and the coin (lets call d).
With this data, height of the tower = D * (h/d)
Around 5 ten rupees coins, because in about 50 rupees I can purchase a LASER light and a protactor, and using trigonometry I can calculate it😎😎😎
U can't see top of burj khalifa by ground so u can't determine angle so u won't be able to calculate though trigonometry but your idea is good and innovative appreciate it!!👍👍
Terminal velocity, air resistance
You need to consider them as the velocity of the city will not increase once it reaches its terminal velocity
Air drag left the chat
Answer No. 2
Place a coin of known diameter on its edge and measure the shadow. Divide the distance of the coin shadow into the shadow of the shadow of the Burj Kaalifa, then multiply by the coin's diameter.
first view
You can also measure the height using one single coin and shadows.
At the same time (preferably at noon when shadows are shorter), measure the diameter of the coin (standing on his edge) and his projected shadow, then the shadow projected by the tower and set a proportion. The solution is
Height (Tower)= height (coin)*Shadow (tower)/Shadow (Coin)
1 coin. Put the coin on the floor, standing in its rim, at a distance where the coin can block the building entirely. Then measure 1) the distance from your eye to the coin. 2) the angle between your eye and the top of the coin 3) the diameter of the coin and 4) The distance from the coin to the building. Then do some trigonometry
Which software did u using for this editing.....?
The answer: 0 coins!
You don't need coins to measure the height of a building at all!
If we did need to use coins as a measuring tool, I came up with the same answer as seems to be popular in the comments: keep it in front of you until the building's top and bottom align with that of the coin, and trig your way into figuring out the height of the building.
If you're ONLY allowed to use coins, no other measurements such as a car's odometer, your own estimations, or timing devices such as a stopwatch, then it becomes harder. In this case, I'd say get a picture with known scale. We are allowed to scale, but not to know the actual height of the scaled picture; that would be an illegal measurement. Then use the coin to see how many coins go in the scaled picture, and thus you know the height!
This is pretty neat because it doesn't allow you to use any kind of non-coin measurement system, it's practical, much more so than dropping a coin from a 500-meter building and somehow registering when it hits the floor, and do this without endangering lives while also figuring out physical constraints such as air friction... Anyway, this works, and it meets the demands and then some!
And, neatest of all, the amount of coins used is still just one!
Cool problem, makes for some very diverse answers!
Measure the angle between shadow casted by coin and the coin, now measure the shadow casted by the tower, we know what ratio of angle it make. So, by using it we can easily find the hight of the tower
You cannot eliminate air friction - unless you have a very long vacuum tube.
But then, you'd already know the length of the tube.
Or, enough coins in a spherical container to negate/minimize air friction to desired accuracy.
One coin ,I will take it to top roof and release it and release it and when the coin reaches the ground,then we know exact time and calculate actual height of building taking drag force in consideration and then apply F=m*a
Among other methods, I briefly considered getting Tom Cruise to throw a coin off the ‘top’ of the Burj. He would have to negotiate that terrifying last spike and hurl the coin with sufficient force to clear the building. A bad, imprecise sort of start but, as I guessed, the real problems start with air resistance. I did some research and some calculations. If a falling coin really did continue to accelerate at 9.8m/s/s, it would fall the 828m in about 12.6s and land at a velocity nearing 4,500kph! IRL a ‘standard’ coin reaches a terminal velocity in ideal conditions of - at maximum - less than 25m/s. The drop would therefore take, depending on the coin’s density and aerodynamics, wind shear effects etc, a minimum of 40s and could take quite a bit longer. You would need to know all these factors to make any calculation. In the end I sulkily concluded that I couldn’t use any practical number of coins to directly MEASURE the height of the Burj as this challenge requires. So I’m glad that - as far as it can be trusted! - the internet will tell me the height for a fraction of 1% of a virtual penny.
One shiny coin and a very long measuring tape:
Look down at the coin at 45° and move away from tower until you see its top in the middle of the coin.
Measure the distance to the tower through the doors to the point exactly below the tip of the tower.
Take a nice coin, ideally a gold or silver one, but any old coin of significant value works. Walk to the receptionist and say "I shall trade you this fine coin if you can correctly tell me how tall this building is. You are allowed to consult other people or sources if you don't know offhand."
1 coin, no dropping. Hold the coin out at arms length, with the bottom edge of the coin in line with the bottom of the tower in the distance. If you know the 'height' or diameter of the coin, and the distance out you hold it, then if you hold it such that the top of the coin is in line with the top of the tower, you can use the ratio of coin height/arm distance against the distance you have to be from the tower to make the coin edges be in line, to calculate the height of the tower.
Answer take a mirror place it under the burj Khalifa so that the reflection can be seen take few coins from your pocket place it on the mirror and count how many coin you need. ;-D
One coin if it is bitcoin.. i can hire a team of expert with all expenses, would cover by one bitcoin...
2nd answer is also one coin, i will tie the coin with a string and hold till it touch ground, so height = length of string
I have another approach to find the length, taking a coin close to initial position and moving a coin at certain constant speed until the heigh of building is equal to the height of coin, this approach will succeed....
By applying the thoughts of image capture😉😉😉😉
One coin, keep coin at some known, constant distance from your eye, keep moving away from the building until the coin covers it completely. Measure the distance from the building to the place where you stopped. Solve for height of the building using Pythagorean theorem
Speed of the wind would be soo fast at that height , thus we never gets the coin in straight line , so this method is very approximate .......
According to my funny logic :
We can go far from building as we can gets the building height equals to one coin ( by closing 1 eye view) .....and making triangles from a point to the coin and building by stretching same line on ground (we knew length of ground we walked) and height of the coin as well ....... Thus by similar triangles properties we can find the height of building ( survey method) ..... using single coin 🔥
The same way you can measure distance of moon if the radius of moon, radius of coin is given. Close one eye and keep the coin between your open eye and moon such that it totally covers the moon. Now, imagine two similar triangles and conclude radius of moon divided by radius of coin is equal to distance of moon divided by distance of coin. One can use the same approach with this problem.
From a certain distance away, just one coin. Then you calculate the height of the building to the diameter of the coin relative to the distance from you to the building and the arm's distance from your eye to the coin.
I go on a tour of the Burj Khalifa. At the end of the tour, I ask the guide how tall it is and then offer a tip of one coin in thanks.
Or I tie a coin to a fishing rod with a very large reel. Then I lower the coin to the ground from the top and measure the fishing line.
Or I throw a coin out horizontally at a known speed from the top and measure how far away it lands. If it is dense enough then it will describe a parabola so I can work out the height. Although this assumes a constant acceleration due to gravity, which is not entirely correct. So, instead ...
... I tie a very dense coin (krugerand?) to a very thin piece of cotton. Then I put it in an evacuated box. I let the coin swing back and forth like a pendulum at ground level and at the top. I check the period, and work out the acceleration due to gravity in each case. Assuming the Earth is spherical and the mass of the Burj Khalifa is negligible compared to the Earth then the acceleration due to gravity is inversely proportional to the square of the period. Gravity is also inversely proportional to the square of the distance to the centre of the Earth. So the didtance to the centre is proportional to the period. So we can work out the height of Burj Khalifa as a fraction of the radius of the Earth.
That equation ignores air resistance, which in this case is very significant. A coin dropped from the tower will reach terminal velocity in the first few seconds, and would actually take (very) approximately 30 seconds to reach the ground. Big error bars on that value, as the size of the coin and actual drag are unspecified. Physics problems love to ignore friction, air resistance, temperature, and other things that often don't make much of a difference to the answer. Unfortunately, that's not the case for this problem.
Hey I may have a better answer
Although answer is one coin but we can have a different approach like
Keep the coin in line of eye such that it covers the tower .
Then measure the distance between you and tower and then find the height tower using tan A where A is angle of elevation of top of tower
Why to go top of tower and risk life
You can measure the shadow of the building at the time when it's perpendicular. Starting from the entrance, an indian Rs.10 coin is of 27mm dia.....27mmx number of flips till you reach the end of the shadow will give you the length of the shadow and then apply Pythagoras theorem.
if we can make an arrangement that the sound of the coin hitting the ground can be heard at the point from where its dropped then measuring that time in stopwatch and using the speed of sound in the air can give the height.
You said using a coin. Your solution uses a coin and a stop watch.
And as others said, you completely ignored the drag force on the coin. What is that drag force? Well, that would depend on the coin you throw off the top (yes, you have to throw it and you would need to throw it horizontally at a significant velocity to not hit the lower floors). And you didn't take into account the current wind velocities. A building of that size will have significant vortex shedding which can greatly affect the "flight" of your coin.
If you're allowed to use other things, tie a string to the coin and measure it's period as a pendulum at the top and again at the bottom. Because of the change in the acceleration of gravity, you should be able to calculate the distance, but that's not very practical either because you would probably need to do this in a vacuum chamber to remove the effects of the air.
I think the easiest way to find out the height using a coin would be to find someone that knows they height and say, "I'll give you this coin if you tell me the height of the building."
1 coin;
Line up a pencil in between the building and your eye so that it has "the same height".
Flip the pencil 90 degrees from the base of the building so the pencil is horizontal.
Let your friend walk to the point where your pencil ends and mark that spot.
Now use 1 coin. mark 1 dot on the edge so you can count the rotations.
Roll the coin to the base of the building and count the rotations.
Now do multiply the rotation by the periphery of the coin. Voila, there is your answer.
I know this isn't an optimal method, but I think it's a nice approach :P
How many coins entrance fee to take you to the top of Burj Khalifa, how many to buy a high precision stopwatch and how many to buy a binocular/telescope to know when to stop exactly measuring ?
Gravity of building is also causing attraction towards the coin.
terminal velocity of the coin makes it difficulty to measure such a tall building. Alternatively, do it like a sniper. Place a coin in front of you to cover the whole building just touching the upper and lower edges of the coin. Since the size of the coin is known, and the distance between your eye and the coin is measurable, the only parameter left is the distance between you and the base of the tower. If you know it by any means, the height of the tower is calculable.
How do you go to the very top of the tower to drop the coin? There is a doable answer. Take a coin of a diameter of let's say 3 cm. Go far away from the tower and put the coin on the ground in a standing form. Put your eye or camera at ground level and go back and forth until you find a spot where the coin covers the whole height of the tower. Calculate the distance between the camera and the coin and the distance between the camera and the tower. The rest is easy. Let's say the tower is 900 meters tall. If the camera is at 1200 meters from the tower, then it looks like we have a 90 meters tall tower at 120 meters away, or a 9 meters tower at 12 meters away, or a 9 cm tower at 12 cm away or a 3 cm tower at 4 cm away. So if a 3 cm wide coin at 4 cm distance covers the whole tower and we are at 1200 meters from the tower, it MUST BE 900 meters tall.
Gravity is not the only force to consider - there is also wind resistance. The second equation of motion calculation assumes that the coin will continue to accelerate until it hits the ground. But a small coin - say a penny - would reach terminal velocity at about 50 feet, so the calculation would not work.
Walk backwards until the coin obscures the skyscraper when it is 1 inch away from your eye then use trigonometry to calculate the height
That solution wouldn’t work, because your friend on the ground wouldn’t know where to look for the coin due to the wind speed and turbulence around the tower. Given that the terminal velocity of a penny is around 22 m/s, the coin is going to drop for more than half a minute and if the average wind speed is 10 m/s then it could drift 300 meters or more before hitting the ground. So if stacking coins is dismissed because it’s not possible in practice, then the coin drop should be dismissed as well.
The best approach (if you have to use at least one coin) is probably to compare the length of the shadow of the coin with that of the tower and use similar triangles to work out the height of the building.
1; place it on it's side, then mark the spot and move it up. Continue until you reach the top, count the spaces, finds the size of the coin and multiply.
I'm very late
One coin. Use the shadow of the building, place the coin on edge at the tip of the building's shadow. Measure the height of the coin, use similar triangles to get the height of the building. This is a simple geometry method, requires no knowledge of physics or measurement of time, and it does not require a visit to the top of the building to drop the coin. It also is not affected by air resistance, as would the dropped coin (which would reach terminal velocity before it was even half way down... your time of 13 s implies the coin hits the ground at a speed of ~130 m/s , almost 300 mph, which is unachievable due to air resistance... or very dangerous to the unsuspecting people below.)
Ancient cultures used the similar triangle method long before humans understood physics.
You can't time a stopwatch exactly one, and even moreso not twice. Gravity isn't exact and different in different places. Air resistance is a thing. How do you practically get on top? You wouldn't be able to drop it right from the tip since the building spreads out and the coin would hit the sides on the way down and get slowed down. The time is also off because it's slightly closer to the ground depending on how the coin is rotated. That's not measuring at all, it's just estimating.
My solution would be to wait until noon, when the shadow is at its shortest. You can measure the length of the shadow along the ground, and you can measure the length of the shadow of a meter stick. Then just do the math to get how tall the building is. Since you can keep flipping the same 1 coin, you could still argue this could be done with 1 coin if you wanted, and it would likely give a more accurate answer. Or better yet, since we can use non-coin things like a stopwatch, why don't we just also use the world's longest measuring stick and measure the entire height using 0 coins? That's my funny answer though.
We can use one coin and at a distance we can see when the coins diameter is equal to height. Then accordingly by the distance we can measure the height by proportion.
Well because of air resistance...it might not give the accurate results. I would rather calculate the length of the shadow of the building, length of the shadow of the coin at the same time and height of the coin(diameter). So the ratio between the height and length of shadow of any two objects should be same at any time. So it comes down to: height of Burj/ length of shadow of Burj = height of coin/ length of shadow of coin. You know 3 parameters, find the 4th one. It might give more precise answer.
Prerequisites: Sun.
Can you just hold the coin at arm’s length and stand far enough away until the coin perfectly covers the building? Simple trigonometry will tell you the height.
IT WOULD ONLY BE CORRECT IF THERE IS NOT A THING AS TERMINAL VELOCITY.
TERMINAL VELOCITY IS A VELOCITY AFTER WHICH OBJECT STOPS ACCELERATING AND ALSO YOU DIDNT consider air resistance.
Useful knowledge bro.