I don't want to sound hyperbolic, but this problem is actually a "cinch" if you think about it. Thanks for 5 million views in 1 year! (Perhaps the most watched math video of the last 12 months on RU-vid, you guys are awesome!)
Some doubts *(1)* If the lowest part of the cable is 20m, the catenary equation is y (x) = 20.cosh (x / 20). Hence, as y (x) = 50, we have 20.cosh (x / 20) = 50, ie x = 20.acosh (5/2), or rather x is approximately 31.33m. Therefore, the distance between the posts is 62.66m. Furthermore, using the arc length formula, we arrive at half the length of this catenary at L = 20 senh (31.33 / 20), ie approximately L = 45.81m. What would give as total length of the catania: 91.62m. In short: if the shortest distance from the wire to the ground is 20m and the wire describes a fixed catenary on the 50m poles, the length of this cateraria is NOT 80m but 91.62m. *(2)* Assuming the length of the wire is 80m, and we do not know the parameter "a" ... Then, using the arc length in half of the catenary, we find senh (x / a) = 40 / a. And, since y (x) = 50, we would have "a" . cosh (x / a) = 50, hence cosh (x / a) = 50 / a. Using the fundamental relation we find (50 / a) ^ 2- (40 / a) ^ 2 = 1. Hence, a = 30. Using this value, we deduce that cosh (x / 30) = 50/30, ie x = 30 *.acosh (5/3), or approximately x = 32.96m. Hence, the distance between the posts would be 65.92m. In short: if the wire length is 80m, the shortest distance from the wire to the ground cannot be 20m. It should be 30m. Where am i going wrong? Note: Sorry for my English. =)
I think part (b) is a clever interview question, as it requires some outside the box thinking, but part (a) doesn't seem very practical unless they expect you to only approximate the answer. I doubt that most mathematicians know the equation for a catenary from memory. To be honest if given this question I would probably just approximate the cable with a parabola and hope that the answer is close enough.
honestly you can even just approximate it with triangles and that's pretty close. All you need is the pythagorean theorum. That gets you to 26.46, which I would probably round up to 27 since we know there's bend in it that will make it longer than a straight line. And if you do this with the second one you'll get the correct answer of 0.
@@NotMyActualName_ that's exactly how I tackled the problem, but keep in mind that you would actually want to round the number *down* for this scenario! Since the straight line would reach further, compared to a curved line of the same length, the maximum distance decreases as you increase the curvature. I think using the Pythagorean theorem for a quick "off the top of your head" reply (acknowledging that it's only an approximation) is a better alternative, as long as you later can refer to Google and other sources to solve this with the proper equations (which I could never remember by heart, and even if I did, I should not trust that blindly, and would have to double check with trusted sources anyway before taking any kind of important decision). It still is a cool math problem though!
I looked at it for a bit a figured I could get close enough with C²-A²=B² and ignoring the tangent might be fine. So I figured A=Height from top of pole to center cable B=Half distance between poles C=Half cable length. I got A²=1600 & C²=1600 and then when, wait - what? Distance between poles is 0? I better finish this video. Then there were all these crazy formulas & I was like damn I must have really messed something up in my reasoning but in the end for 10m version my 30sec solution actually was right. But for 20ft height I would've said 50ft apart and been off by 4.6ft
In the interview, I would say we approximate the cable with a line and take x = SQRT(1600 -900) = 26.45. We then multiply by 2. You can also easily see that the second one will be infeasible because it gives us zero distance.
I am a mechanical designer of 0ver 30 years, been to lots of job interviews, and was hired by many different companies, and I never once encountered any problem like this in any of my interviews. That Amazon would use such a problem in an interview seems totally absurd. Does Amazon hire overhead power transmission line engineers?
For the 10 meter case, if you draw a straight line from the top of one support to the lowest point of the cable, its length has to be less than 40 meters since the cable is a curve. Draw a horizontal line from that lowest point to the same support. Then you have a right angle triangle with a hypotenuse which is less than one of its sides. So the picture, as drawn cannot make sense. The only case which is feasible is when the cable has no curvature, i.e. it is vertical up and down. So the two supports have to be coincident.
And even then it requires an infinitely thin cable, which means it has zero mass, which, combined with the fact that it has no curvature, means it won't curve as it gets pulled down. The most logical explanation for it having a single lowest point is that the cable is a straight diagonal line to the middle, which means you can use a much simpler formula: you're basically calculating one side of a triangle. For the 10 meter case the answer now is possible, but this also changes the answer for the 20 meter case. We have a triangle with a diagonal side of 40 meters and a vertical side of 30 meters, this gives us a horizontal side of 26.46, for a total distance between poles of 52.9.
I was worried about replacing my high-end older oasis with this one ru-vid.comUgkxCgPI5O2AtmcHq9SJhgsCGbpAzJAJfrJp but it is surprisingly light and the screen resolution is just as good. I never had the warm light on my old kindle, but i do not use it on the ipad so I will probably not need it. I think the only thing I'll miss is the self-adjusting light, but this is so worth it!
Lol, this is not an interview for a dead end job. These people were not interviewing to deliver boxes. This kind of problem is asked in tech interviews, so it would be for software engineers, data scientists or mathematicians. They are for jobs that pay over 100k a year as initial salary. The selection process is usually composed of several interviews. These are not the "talk to someone in HR" interviews. They usually consist on problems designed to test the technical skills of the participants. This kind of interview process is standard in big tech companies, google, apple, facebook, amazon...all the big tech companies follow this type of process.
Sounds similar to the question they gave me; "if the bottle we need you to piss into is in the passenger footwell and you are strapped into the driver's seat of a standard delivery vehicle, at what angle of inclination do you need to aim to manage to get most of it into the bottle?"
My high school math teacher warned that a catenary is not a parabola. The famous Gateway Arch in St Louis a catenary, not a parabola. People make this mistake because they have had elementary algebra but not hyperbolic functions, so they think it's x-squared.
@@michaeljarosz4062 Every physics students learn the calculus of variation in their classical mechanics course. Where they solve this hanging chain problem by using Euler-Lagrange equation.
Who else thought of using the Pythagorean Theorem here, treating the cable as the hypotenuses of two right triangles, with their bases being a horizontal line tangential to the lowest point of the cable. This may not be as accurate, since we're simplifying a curve into a straight line, but it should be a good approximation and Amazon would probably still appreciate our approach to the problem.
Yes I tried this originally at first. Even though a simplification you can still find the trick that when you work out the numbers, the vertical and horizontal lengths of this triangle would both be 40, so we know something is up, and deduce the other length must be 0. I kind of got to here but didn’t think it was a trick question or say 0. Still glad I could actually think of that though lol.
Before watching the video, I did exactly that and got 0 as a result. I thought I was wrong because of the thumbnail, only after I opened up the video and saw the image was made by the channel and that it was not provided with the question I understood what was going on
Fifteen seconds? What, do you think money grows on trees? Clean your Reusable Amazon Warehouse Employee Diaper (TM) in your washer/dryer when you get home.
When drawing the diagram at 4:33 you can see that cable is 40m to the center and the pole is 40m above your x-axis, which intuitively doesn't work. Visually you can see that x would have to be 0. But who would stand 2 poles beside each other and hang a cable between.
I know a catenary from a parabola, but is all I remember about math at this point in my life. Years ago I took the GRE and got tentatively accepted to a graduate math program, but if one doesn't use it, one loses it. These are great refreshers.
This is great. I teach physics and from part a, without really doing any math, I guessed it would be around 50 using a flawed thought process of using the pythagorean theorm, which 45.4 rounds up to. But with part b, before I thought about how to work out the problem, I thought to myself, "why is the cable so far down? That makes no sense," and I didn't have a mathematial guess for myself. So seeing you explain it all is pretty funny.
Good point, I'm not a math expert at all, but also the fact it droops down over half the radius. It is an elliptical, half would be 25m, so it droops with 20m left. So the shorter diameter part of the elliptical (idk the correct term for this) connects the two poles. If it drooped 25m, it would be 50m apart, but it falls a little longer at 30m, so the poles are less than 50m apart, and probably not too much more. From that alone one could guess btwn 40-48m or so.
Amazon's minimum wage is $15/hour and its illegal to pay less than time and half for any hours worked over 40 in a week. Amazon is bad but not that bad
Is 12 dollars or 15 an hour bad? Thats more than what I earn in my country lol and I have a "decent" position working as a financial analyst. And everyone makes similar to that..
I interviewed people for 6+ years at Amazon. I never once used this type of question. None of my colleagues ever used this type of question. We were never trained to use these types of questions (the training actually encouraged us to dig deep into actual candidate experiences related to the area we were hiring for). Only one time did I ever even hear of someone at Amazon using this type of question in a phone screen, and it struck me as odd because this is not the kind of interviewing Amazon conducts. So PSA: don't assume this is the norm.
I believe companies rely on knowledge tests to much and miss out on the people who have natural talent to do or learn better than someone who has all the right answers. Thinking out of the box is a talent that you can't get out of a book.
@@webyankee6558 To add to this, I'm a scientist myself, but I don't memorize any of these kinds of formulas. If I use something frequently for a time I might, but that's it. Pretty much any kind of formula needed is readily available with a quick search on the internet, or in a book, etc. That's the benefit of technology. If I were the hiring manager, I would care more about one's ability to use the resources available to them to solve such a problem than the fact they memorized formulas to look smart.
Amazons first question during the interview…. “Can you breathe on this mirror?” “Ah, ha.. i see you in the mirror and the moisture confirms you are alive.” “You are hired”
@@webyankee6558 this problem relies on someone memorising a formula. There is a way to solve it using physics from first principles (force balance along cable) but without being given values for, presumably, a spring constant, you could only derive general solutions.
Someone posted this on Facebook and after I figured it out to be 0 m, I found this video to see how other people processed the question. The way I processed it: Half the cable is 40 m, which is half the 80 m cable and also 50 m - 10 m = 40 m. So if I keep raising the bottom by 10 m until I get to the 50 m height of the poles, then eventually I get to 0 m for half of the cable. So the poles are 0 meters apart which is nonsense regarding the actual picture. lol
I'm a naval architect so I've come across catenary problems many times with anchoring. I have written numerical methods that solve it (because in this day and age it's quicker. Then I saw the 1st problem at the end and instantly saw that they must be zero distance apart. If it wasn't after 10pm I would have done what you did and taken 10m from the bottom and come to the same conclusion
am glad i made it in 3-5 seconds using pythagoras square triangle formula. i knew it was an approximate but i soon noticed square of hypothenus was equal of square of the pole length, it is 40^2. then the other side should be 0 in length !! or pythagoras had been tricking me for my entire life ! lol ! thanks ! ayala & yami, shamanes associate
Quick approximation would be Pythagoras. a²+c²=c². We know one side with the pole height(30 resp 40 meters) and the hypothenuse with cable length/2 as 40. That means for cable hanging in the middle at 20m we have 40²=30²+b² which can easily be solved
Well, but if we ask you to draw this in an interactive chart, with one pole able to move sidewards, you are back to business ? The answer to the original question will only be a side-output then.
How is this a non sense?? If you don't know or like Maths, does that make this useless? Humanity's tech keeps rolling only because these are people who know Maths very well.
@@yashsvidixit7169 No sorry, it's nonsense to memorize a formula you need once every 10 years. This ist old fashioned thinking to store everything in your head. It's allowed to use "external storage" like Wikipedia to look up, when needed. I mean, some exaggerate and need a calculator to compute 5*7. But computing 312*28 in your head, you can do for party entertainment to impress people, no job should depend on that ability.
Here's the generic solution: Catenary equation: y=a*cosh(x/a)-a+h take the derivative and plug into the arclength integral... dy/dx = sinh(x/a) L = int(sqrt(1+sinh(t/a)^2),t,0,x) = int(cosh(t/a),t,0,x) = a*sinh(x/a) square this equation then use identity (cosh(x)^2 - sinh(x)^2 = 1) to rewrite. L^2 = a^2*sinh(x/a)^2 = a^2*(cosh(x)^2 -1) now manipulate and square the catenary equation... y-h=a(cosh(x/a)-1) (y-h)^2 = a^2*(cosh(x/a)-1)^2 Now divide the catenary equation by the squared arclength equation... (y-h)^2/L^2 = (cosh(x/a)-1)^2/(cosh(x/a)^2-1) using the exponential form (definition) of cosh(x) you can rewrite the right side... (y-h)^2/L^2 = (cosh(x/a) -1)/(cosh(x/a)+1) define b=(y-h)^2/L^2 and solve above equation for cosh(x/a) cosh(x/a) = (1+b)/(1-b) Plug this back into the original catenary equation... y = a*(1+b)/(1-b) -a +h and solve for a... a = (y-h)*(1-b)/(2*b) because we know cosh(x/a) = (1+b)/(1-b), and we know a and b, we can solve for x. x = a*acosh((1+b)/(1-b)).
Warped Perception of you knew 10,000 equations you’d be alright. Don’t worry dude I mean yeah you have to be a genius to do this but you don’t have to do this to be a genius.
It took me about 45-60 seconds of thinking, but I'm nearly positive I know the answer, at least to problem b. But a would require more math than I'm willing to do right now. Though, if I'm not mistaken the shape the cable would make is a hyperbola. *Edit:* Almost right. :-) I was definitely right on b.
I guess the proper solution of 20m version should include deducing the exact function that describes the curve, based on forces of gravity and tension working on a unit of wire, and then taking an integral.
The curve is... a hyperbola. That's the common starting point here. As MYD points out, you just need to look up the equation for a hyperbola and solve it at the known [x,y] coordinate for the constant.
@@kindlin how do you know it's a hyperbole? It's your assumption. You must deduce the formula itself, this is the essence of the problem. The rest is just calculation a monkey can do.
@@phobics9498 Unfortunately a cable does not hang in a parabola, that's more like projectile motion, as a classic example, a parabola is much easier to work with. No, a uniform, prismatic, tension-only cable takes the shape of a catenary, which is mathematically defined with the hyperbola. It does still have a closed-form expression, tho, so there is that. EDIT: A prismatic member has the same shape and material along its length; so, it's redundant with uniform in my list, as the the definition of prismatic means a _uniform shape_ and a _uniform material_ along its length. Anyways, I just had to clarify that.
Yeah i find that way more interesting. This can be "easily" solved by taking the langrangean (or hamiltonian) of the system and obtaining the stable points, wich would indeed be described by an hyperbolic function. Then, it's just a problem of describing the initial conditions of the system.
@@beau6113 Exactly. Most likely, this isn't a required Q & A to be a delivery truck driver. Yet you should always be courteous to anyone who provides you a service you're too lazy [not in the case of disabilities or other hindrance] to go to the store & get yourself. Kind of like a sit-down diner, restaurant or bar. 😁
JKay11235 yeah but Paul said linearize which means your answer is an approximation. I disagree with the answer because linearizing shows you that part b is just not possible because it's an impossible triangle, but it's still a fine start to a problem if you don't have random shitty formulas memorized
JKay11235 that's why it would only be an estimation dumbass. Don't know why Amazon would expect people to be familiar with hyperbolic functions if they're just going to be moving boxes all day.
Shraydn ok I have done so. To my understanding, it's just a specific triangle that serves the same purpose and yields the same result as thinking of it as a line in this case. The line is oriented directly downward if you want to be extremely specific
I've had numerous engineering interviews over the years, some of them lasting an entire day. You can't overthink stuff like this because you're not expected to actually start remembering esoteric equations out of thin air, and solving them. They are critical thinking questions. They want to see how your brain works, not your mathematical recall. Cable is hanging 40m below the top of the poles. Cable is only 80m long. So cable is basically folded in half. Distance between them is 0. Pretty basic stuff.
When i saw the thumbnail i thought of just using Pythagoras theorem will solve the problem But when i started to calculate hypotenuse came out equal to altitude 🗿 As altitude cannot be equal to hypotenuse so they must be coincident That's it problem solved 🙂
I found a slightly quicker method. I got a friend to help me with 2 50m long poles with an 80m long cable attached at the top of each pole. Then another friend measured the distance of the drop of cable in the centre between the 2 poles I and my friend were holding. Once it reached the required height from the ground we just measured the distance between the 2 poles! Easy and certainly quicker than doing the maths...
@@xenomorph6961 You wouldn't get the job. They only want to pay people from the neck down. They don't want you thinking outside the box or anywhere else. They just want you to fill the box with product and send it to a van.
Ha but if you were asked the amazon question of 10m..you can solve it easily with zero maths in about 2 minutes. Meanwhile you'd still be playing with many friends, rented in construction equipment to erect two 50m poles! (Hint buy 60m poles so you can have at least 10m in the ground..and about 20 bags of postcrete mix!)..perhaps you could scale down and use 2*5cm drinking straws and an 8cm bit of string! But still..the answer is zero!
... They're asking this as an interview question? For what? This is something I used to give as a homework problem for advanced freshman physics. I can't imagine what it would tell you in an interview setting.
Yonatan Zunger it tells you the same thing it tells you about your freshman student. It tells you who can think, not just crunch numbers. BTW, I didn’t realize it either, so I guess I’m not as smart as I sometimes like to think I might be.
I suspect that (barring the fact that this was a trick question), the point of asking these questions isn't to see who gets it right, but the method people use to try to solve it. If someone just immediately throws the towel into the ring it tells you something useful (and you probably wouldn't hire them). If someone gets as far as splitting it at the centre and the coordinate system, but then doesn't know the right equation for the cable, of if they take some time to approach the problem in another organized way it tells you something about how they think. Someone actually immediately solving it would actually be a disappointing result, as all it tells you is that the person was familiar with the question.
Like many others have commented, I calculated the answer as two hypotenuses. Considering that this question was asked in an Amazon interview withouot concern for higher math, I must assume it was designed as a practical application of 8th grade geometry.
You can estimate the 20m situation with Pythagoras. You end up with a right triangle of legs 30m (50-20 for the pole), x, and a quasi-hypotenuse of 40m. 40m is longer than the actual hypotenuse, because of the curvature of the cable - it does not follow the straight line distance between the top of the pole and the midpoint of the cable. But let's say we say "I don't know the caternary formula, by Pythagoras gives me a good first estimate." I think that's reasonable. 30^2 + x^2 = 40^2. 1600 - 900 = x^2. x = sqrt of 700, which is about 26.45m. The actual hypotenuse being shorter than 40m, you would say 26.45m (times two to get 52.9m) represents an effective upper bound on the answer. To get a lower bound, assume the cable has infinite mass and infinite tensile strength, such that it immediately droops to 20 meter off the ground, and then stretches parallel with the ground before reaching the other pole. Now you have a rectangle, with an x distance of 40 meters across (80 - 20x2 for each drop). So you can say for certainty that the distance must be between 40m and 52.915m. And the actual value of 45.4m ends up pretty well smack in the middle. Not exact, but quick, and not bad for basic math.
I believe the accurate answer to the 10m question is ""The cable would not be only 10m above the ground". The 20m question assumes a parabolic curve, which recognizes the physical characteristics of a cable, whereas the 10m question ignores the fact that any cable, no matter what diameter, must bend into a curve when turned back upon itself, reducing the effective length. Therefore the 80m will always be more than 10m above the ground. Of course, one can assume the ability to pinch the bend, but one could just as well assume a heavy enough weight to make two straight sections in the 20m problems, and therefore a simple trig solution.
I'm glad I didn't wasted more than a minute to try to solve this problem and moved on to see the solution because I would have never solved this problem.
Most companies hiring for a semi-numerical role (i.e. pretty much every role in a technical firm) tend to ask questions like this one from my experience. This includes 99% of the financial services firms plus their competition in the hiring market (i.e. the tech firms like Amazon, FB, Google etc). The outcome of the interview is a function of the number of candidates versus how quickly they want to hire versus how long the hiring manager wants to stay with the firm. If there is only a few candidates, they are desperately looking and the manager is on his notice period expect a quick hire even if you don't know what a meter is. On the opposite end of the spectrum, expect not to be hired even if you are Einstein himself if they are not too serious about hiring (whether they know it or not). So how can they not be serious about hiring yet be conducting interviews? a) they are gathering street intelligence (they want to see what the competition is up to and what kind of people are they losing and why) b) they have the budget to hire and the HR has asked them to do so but the hiring manager can't be bothered - yet he likes being pampered by the recruitment agencies c) rejecting a candidate with a PhD that can pluck unicorns out of thin air and he is cool and experienced boosts the superiority complex of the hiring manager how might be a school drop out who just happened to be stuck with the firm because he has nowhere else to go. Despite what they want you to believe, most firms, and that includes big investment banks, have zero guidelines around the exact questions that can be asked other than things that can land them in a lawsuit (e.g. are you pregnant?). Therefore, the hiring manager most of the time asks what their ego dictates including questions like this one. When all is done and you are hired after 10 rounds, expect to be spending 99% of your time raising JIRA tickets and writing 0 interesting code with any sort of direct impact to the firm.
As someone who taught geometry at one time and took refresher courses in multivariable calculus, I only watched the intro to the video, stopped it and calculated then watched video. The cable 20 m above the ground approximates two hypoteni (the plural of hypotenuse) of right triangles, which would make each hypotenuse 40, one side of the triangle is the pole from 50m to 20m which is 30 m and which would make the width of the middlle of the cable about 26.5 m from each pole by the Pythagorean Theorem x =sqrt(40^2 - 30^2) = 26.5 m. So it's about 53 m from pole to pole. That is in the ballpark of the calculation in the video, which is so complicated it requires trig functions and the quadratic equation, that I don't think there would be time enough to do in a job interview unless you were being interviewed for an engineering position and were given a test, not an interview. The 10 m is a trick question. In order for the cable to be 10m off the ground, there would be no distance between the poles because half the length, 40m would hang down from 50m height of each pole accounting for all 80 m of cable
But the trick in the question for a) is precisely that you're asked for it to be correct to a decimal place, which means that linearising the curve would not work. You can see that because your answer is not even correct to the first significant figure. Even part b), because it's asking to a certain number of significant figures, makes you start trying to calculate. Which is obviously why it's a trick, and requires simple addition to solve if you think to picture it.
ive seen it on instagram, i think its exactly a question for hiring engineers. i dont wanna sound cocky but i had it in like 5 minutes. these kind of calculations is what you do on a daily basis in all kinds of engineering classes.
I saw the thumbnail and thought to myself… If I was asked this in an interview; I’d say: “that’s close enough to a right triangle for me, we’ll just use a squared plus b squared” And then when I did it on a notecard I found out that for the 10m problem the distance would be 0. “Whoops guess I’m not as clever as I thought. “ Watched the video and was pleasantly surprised… By the end of it. Hahahahah great video, mate.
I got similar results from considering the sagged cable to be in perfectly still environment as a semi circle (180 degrees of a circle with 160 M circumference) with the bisected midpoint 20 m off the ground for my mental image. Then I overlaid the Pythagorean Triangles to orient the poles & radius of the Semicircle. I calculated by hand solving for B or Radius & confirming by plugging the values for either the B side from Pythagoras Method into the Circumference Formula (C = 2πR) where 160 m as C is known & 3.14 for pi. The second problem was a problem from the mental image because even changing the curve to a parabola opening UP, the gross measurements of the beginning diagram were not possible to have both the length of the cable stay at 80 m & the poles 50 plus the limiting factor of a 10 m gap from the ground. Before getting into harder math it was clear the original diagram had to be altered. I am certain this was more of a "how do you handle a stressful situation" exercise, problem -solving skills & communication exercise plus perseverance & the measure of out-of-the-box thinking. I think it's important (at least for me) to understand the "how" & "why "of answers of one cannot recognize an figure that may be orders of magnitude wrong. I don't ever want to have to calculate Sine & Cosine even with a slide rule & found the simpler methods enough.
I had a similar interview question that wasn't quite as unpractical or unrealistic as this one. Mine was to determine how many laptops could be stored in the belly of an airplane for transit. Average plane, nothing military, commercial passenger aircraft. I needed to walk through my mental calculations out loud so the interviewer could hear my thought processes in arriving at an answer. By walking through what I'd experienced in the size of the laptop boxes, normal pallet size, and approximately how many pallets could fit underneath a plane, I got pretty damned close to the actual measured and calculated answer. In fact I was SO close to the actual answer, the interviewer was stunned. No one had ever been able to get that close just verbally walking through the variables. Still didn't get the job...
That's way beyond what an Amazon interviewee could reasonably be expected to know. However, the curve is very close to a straight line, so we can get a very close approximation with pythagorus. Which would be a LOT more reasonable to expect.
I figured it would be a question for high end positions, But if that question is for any and every applicant, that means If you Answer It Correctly, It will definitely will ring a bell , There's a purpose for it.
@@steventortora4487 when box handlers put 40 pound kettlebells onto the wrong belts to where they fall off and kill a man(yes this happened) you start to consider the thinking ability of your employees
Interesting. I took a totally different approach, by attempting to apply the pythagorean theorem, while chopping up the diagram into triangles, and I basically came to the same conclusion. The problem I ran into is that I thought I was doing something wrong, and never bothered to really look logically at the situation. For most of these kinds of problems, my number-one problem is confidence in my findings, and that's something I really need to work at.
@@AlgoTradingX that's because the Pythagorean Theorem doesn't account for the curve at the middle of the cable. I went the same route initially but had a feeling that it would have a measure of noise because that theorem assumes perfectly straight sides.
Cut a piece of string 8in (or 8cm) long then cut 2 pieces of string 5 in long to represent the poles. Place the 8in string between them and move them together until the 8in string center is 1in up from bottom of the two 5in poles.
@@AZStarYT High school and college was a long time ago for some, and for others even still, like I never truly understood Quadratic equations. Im sure Im part of a large, sizeable group who could use the explanation.
@@AZStarYT Maybe he didn’t. I certainly didn’t get this kind of tuition. Does that mean I’m not allowed into the club of being able to enjoy this video? You g gate keeping with your high school education?
@@EvelcyclopS I guess all this points up the huge difference in high school education back in the 60's (and COLLEGE in the 70's) and what passes for "education" nowadays. Totally lacking in the basics. Seems the Communists at the NEA won.
No one ever uses Hyperbolic sine and cosine in high school besides maybe just a hint at the fact that they exist. Not even in college, anywhere besides in a Math degree you'll see those. The point of the question was to not try and find a mathematical solution, but use lateral thinking. And it does a really bad job at that, 'cos it's worded to hide what they want.
The rope between the 2 pillars should be around 60-65 m the length that needs to be cut off of the rope is around 15-20 m. Without math , took the size of the 10m mark, put the 50m pillar on its side towards the other pillar and used the 10m size to find the missing distance.
I believe this is my first ever youtube comment in nearly 20 years... I'm so disappointed that a mathematician broke out an applied engineering formula without deriving it. I've watched many of your videos and can't remember another instance of no derivation/proof. What you did was closer to Googling the answer than solving the problem.
I'm with you on this. This should have started with a proof showing that the cable-mass doesn't affect the shape. Then derivation of the shape formula.
•The best thing I've found so far! I found this when looking for actual, demonstrated use of hyperbolic functions. The amazon, 10 meter "trick" was just a bonus. •I was never taught hyp trig (nor heard of it until I saw it on a calculator function), but I know regular trig well, so why gap my knowledge here? •Most others' videos are just a list of applications or some diagram without much real, how do you *use* it explanation (and where does hyperbolic angle come in, how is it linked to e^x functions in growth /interest rates, other not so obvious applications etc etc).
@The Golden Legend The reason he didn't show it was because it requires physics to derive a differential equation for it and then differential calculus to solve it.
I kinda arrived at this conclusion due to first simplify the problem (ignoring any curvature and assume the cable is straight and bends once) effectively turning the problem into a triangle problem. Now I didn't think this would do anything but give me an approximation to work with, but an immediate problem based on this approach (involving the need to only look at half of the diagram) you have a right-angled triangle, where you know that the height is 40m, but the hypotenuse line (across from the 90 degree angle) also is 40m (the longest the cable can be, since it is under no curvature). That is of course impossible, unless they are the same line and it is not a triangle at all but a straight line. Which means the problem, only works if 2 poles is one pole and no distance and no area can be in between. Effectively arrive at the answer. Lucky maybe, but works.
Actually, I did the same before watching the video. Then I tried doing it for case a) and got a different value, but it's comprehensible when you think about it: if you have actual distance between the two poles, there is a curvature in the center of the hanging cable, but if the two poles are together/only one, that curvature doesn't exist, thus making the two right-angled triangles approximation actually accurate.
@@cloud_strife8 If you solve case a assuming the cable is two straight lines, then use pathogens theorem, the answer you get is within 0.2 meters satisfying the requirement to be within one decimal place.
I started typing this in, as I did the same, but then saw you got that, too. I wouldn't call that lucky but smart way to simplify a problem for approximation, which is very helpful in many cases. @william meek: It's not that accurate here: For the 20m case that gets to 40^2 - 30^2 = x2, i.e. about 26.5m, which is not very close but gives a first idea. Closer is assuming the cable as lower half of an ellipse. Circumference U is approx. pi * [ 3 (a+b)/2 - sqrt(ab) ] with a and b being the longest and shortest half diameters (admittedly had to look that up, too, but this equation is a bit simpler than the one from the video. If a = 50-20 = 30m, then, filled in, b = 20.4m, i.e. 40.8m distance between poles.
@@christophstegert8386 ya the whole "get within x percentage accuracy" kinda tricks people into thinking they have to use some method to approximate the curve and calculate a number. EVILLLLLLL hehe
It works to a degree. The longer the distances the larger the error. For this problem simple Pythagoras gets you to the solution very quickly and easily.
b) I would start from b. And as you correctly mentioned the distance is 0m. a) *When the distance is 0m the rope is hanging 10m above the ground. *When the distance is 80m the rope is hanging 50m above the ground. *The rope will be hanging anywhere between 10-50m above the ground. *Given the above, when the distance is 40m the rope is hanging 10+(40/2)=30m above the ground. *And when the distance is 20m the rope is hanging 10+((40/2)/2)=20m above the ground.
for the b variation im pretty sure you can solve it using the pythagorean theorem because the pole is 40 meters high and the length to the center is 40 meters so 40 squared minus 40 squared is 0
I was actually wondering why such question is included on the interview, whereas this may be more appropriate for a test. Interview should focus more on the behavior quewtions and analyzing a candidate's employment history
But still, this question can help you find those who can think, instead of just crunching numbers. Moreover, being interviewed is also a show. So it's fair if the interviewer is playing the game too.
It’s what happening when you give one side full power without regulations. Add your average student to a position like this and you have your circus show. Laws must always protect the people first, then the interest of companies.
I'm an engineer and I don't even remember my hyperbolic equations. I look them up when I need them. If you get this in an interview, draw the same diagram, and then use pythagoras and tell them it's an approximation. If you work it out, you'll find the answers are close enough (like 5% error). Granted, the longer the cable, the more error you incur. That way you demonstrate you can use high school level math to approx solve an actual problem you might encounter if they asked you to hang a sign.
@@DanSlotea just what I did, in the real world a hanging weight would be pythagorean with the cable strectched tight surely? ...this 'cable' is more like a cantilever beam in it's bending ? not suprised their corporation tax is so low!
@@brendanoneil3489 funny how the same Pythagora's quickly triggers a red light in the second problem, where the visual representation is intentionally wrong to trick you. As soon as he put the numbers I was like what the hell?
if someone got the answer in the amazon interview, they didnt get the job bc they are overqualified and smart thinking people make it hard to exploid them with low wages.
@@pizzablender My statement is still true. Amazon cannot force anyone to work for them or accept a wage they deem too low. I try to buy locally from local businesses, but they rarely cater to me, which is fine, they must focus their resources where they deem appropriate, just don't blame me for not buying goods I don't want.
Interesting question. I tried to get a rough approximation using the pythagorean theorem and found there was no solution to the 10 m variant. The problem with the problem is two fold: Did the problem show your visual from the thumbnail? If so, that biases the reader. We would be hard pressed to assume zero distance with that visual evidence in front of us. If there was no picture, then the issue has to do with common sense. When have you ever seen two poles right next to each other with zero space in between them? How about all that plus a cable? Most people would have trouble even considering such a scenario because of how ridiculous it would be. I understand companies are looking for “out of the box” “creative” thinkers, but as someone who constantly finds better ways to do things, I don’t think this type of problem is good at all. I want people to consider real evidence, not just an absurd mathematical conclusion. Plenty of people have ideas, few people execute those ideas into a workable practical reality.
The real question Amazon would ask is, "how many bathroom brakes would you need during your shift?". If you answer is anything other than zero, you didn't get the job.
@@d.bcooper2271 Exact answer = 45.2m. Pythagorean triangle = 52.9m, estimate down to 50m which is off the exact answer by only 10%. We can do the exact stuff later, but in a job interview or a team discussion no one has catenary equations near them and they don't have to. That is how a real engineer does it in preliminary design.
@@dercooney It doesn't work for part (a), where the cable is 20m above ground. In this case, the distance would be at most 50-20-80/2 = -10m, but the correct answer is certainly more than _negative_ 10 meters. :-) I estimated that the distance must be less than 2 * sqrt(700) = 52.9m.
No - you are a mug because: You had to build the thing trial and error to measure it. You had to wait for delivery You spent money on getting the lazer distance meter. Your DONE takes too long.
For anyone wondering where the half-cable equation came from, it is derived by plugging the function modeling the cable into the curve arc length formula, with the bounds of integration being 0 and x with respect to t, and equating it to 40.
