Ekene Franklin's messageboard.

Feel free to discuss anything here with me friends! We're here to help each other!

Note by Ekene Franklin
2 years, 1 month ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

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My country's national olympiads 1st round is to be conducted tomorrow. I will most likely post all of them here for our consumption! I expect them to be pretty easy.

- 2 years, 1 month ago

Ok. Thanks and also are you writing that exam.

- 2 years, 1 month ago

It is actually meant for students two years older than I am, but I will give it a shot.

- 2 years, 1 month ago

Oh !!!

- 2 years, 1 month ago

It there a minimum age requirement to be eligible to write your country's olympiads?

- 2 years, 1 month ago

Yes, I think it is 13 or 14. People from class 8 or 9 onwards can write the exam.

- 2 years, 1 month ago

Are you also writing the olympiads soon?

- 2 years, 1 month ago

No. At present I am not interested. The main goal of student student studying in class 11 and 12 in India is to get into IIT (Indian Institute Of Technology)

- 2 years, 1 month ago

Oh, so that is what JEE and IIT are all about. I hope you get into it seamlessly. But say, do you hope to write olympiads in the future?

- 2 years, 1 month ago

Yes. I may.

- 2 years, 1 month ago

This is a marvelous secret and I benefited a lot from this. If you want to write any question for the problems of the week the better option is to write a physics problem rather than maths. Out of 5 problems 3 are allotted for maths and 2 for science. In the maths category there will be a much competition from many users. But in the science category there are only 4 competitors namely Rohit Gupta, Pranshu Gaba, and two staff members Blake Farrow, Danielle Scarano. So, I posted some good physics problems and 3 of them are featured now. But I won't force you to post only physics problems then there will be much competition for science. If you have good problems in maths you can post them (as 3 of my maths problems are also featured although I say that I am basically a physics man).

- 2 years ago

Where is the show full site option??(from ur mt. Everest Q discussion)

- 2 years ago

It will be in the main option bar. It is the place where you can find links like "profile", "stats", "search", etc. The "view" full site option will be present there.

- 2 years ago

Main option bar : Those 3 lines on left corner?? Or in the stats section of taskbar?

- 2 years ago

The three line aside the option "Premium"

- 2 years ago

Oh so this is on website. Can this be done in app?

- 2 years ago

Ohh !! You are doing in the app. Sorry, I don't know whether this is possible in app or not. But can't you find any option like this. in the screenshot.

- 2 years ago

No :-( how can I send screenshot on this chat?

- 2 years ago

You have to copy the link of the picture and paste it here.

- 2 years ago

K thnx a lot for helping, and sorry for disturbing..

- 2 years ago

It's OK. No problem. I went to brilliant only once in the mobile app so I am not much aware of the options present in it.

- 2 years ago

Mauj Rajpal, from which part of India are you from.

- 2 years ago

Delhi ;-) and u??

- 2 years ago

- 2 years ago

Oh nice. From where do you put your problems in sets(source) and how do you have sets of other people in yours??

- 2 years ago

In every set there will be a option at the bottom called "save". If you click that, that particular set will be saved into your sets. Some of my problems are original whereas some other are completely taken from books or the problems and the remaining are the problems which I have taken from books and modified them.

- 2 years ago

Can you suggest me some of your book(especially maths)

- 2 years ago

It's our college material. It is a collection of all good problems from various books.

- 2 years ago

Here is the screenshot of where is it present. Can you find it now ?

- 2 years ago

Is this screenshot from app?

- 2 years ago

No. It is from from the main website.

- 2 years ago

How do you send questions to them to select for weekly problem??Do they themselves select from your sets?

- 2 years ago

No. Only staff will select the problems of the week. In general, the notification will be as if I have written the problem of the week.

- 2 years ago

They themselves select it by seeing your sets or you send them via some forum and then they choose one of the all sent questions??

- 2 years ago

The community members write problems and post them to community and the staff selects the best 15 questions among all the problems and they will feature them as problems of the week. There is no forum involved in this process.

- 2 years ago

I personally think Brilliant should include a biology and biochemistry section. What do you think?

- 1 year, 11 months ago

Yes.

- 1 year, 11 months ago

Before brilliant used to have biology. But recently when the staff updated brilliant they removed biology topic due to lack of problems in that category.

- 1 year, 11 months ago

Actually I asked them to remove it, because the biology problems could not be seen in the community page. You can see Calvin Lin's messageboard.

- 1 year, 11 months ago

@X X Calvin Lin's message board is currently unavailable. I searched for the website for a long time but in vain. Maybe he have locked it.

- 1 year, 11 months ago

Really? Here is the link. It's still available.

- 1 year, 11 months ago

@X X But last time when I went it was locked

- 1 year, 11 months ago

yes

- 1 year, 11 months ago

Here is a link of a biology problem.

- 1 year, 11 months ago

Yes, but they cannot be found in the community page.

- 1 year, 11 months ago

@X X I know. And there is no biology when you're making a problem.

- 1 year, 11 months ago

@B D Previously there was, but they removed it.

- 1 year, 10 months ago

@X X OK

- 1 year, 10 months ago

- 1 year, 11 months ago

Hello Everyone !!! As this note has got some immense response from young students I would like to continue this further. But the problem is that this note is getting more and more comments day by day due to which the process of loading and opening any notifications is taking more time. So, on the request of @EKENE FRANKLIN any further discussion can be continued in the new note Brilliant young students messageboard

- 1 year, 11 months ago

$\text{Doubt : 1}$

If the mole fraction of a solute is changed from $\dfrac14$ to $\dfrac12$ by adding some solute in the $800~g$ of $H_2O$ solvent, then what will be the ratio of molarity of the two solutions ?

- 2 years, 1 month ago

$\text{Doubt : 2}$

In the following reaction : $\large aNO_3^- + bCl^- + cH^+ \rightarrow dNO + eCl_2 + fH_2O$ find the value of $\dfrac{a^2(b + c)}{d \times f}$

- 2 years, 1 month ago

Simply balance the redox equation and substitute the stoichiometric coefficients of the balanced reaction into your expression.( I would have posted a solution if only my device could type LaTeX.)

- 2 years, 1 month ago

Ok. Try now after keeping it in \ (....) without spaces which will give you $...$

- 2 years, 1 month ago

Did you tried it. What is the answer you got.

- 2 years, 1 month ago

Yeah, I solved it. My answer is 7.

- 2 years, 1 month ago

That's correct answer. Can you atleast keep the values of a,b,cd,e,f.

- 2 years, 1 month ago

a=2, b=6, c=8, d=2, e=3 and f=4

- 2 years, 1 month ago

Ok. Thanks i will check with mine.

- 2 years, 1 month ago

$\text{Doubt : 3}$

Uncertainty in position and momentum are equal. Then what will be the Uncertainty in velocity ?

- 2 years, 1 month ago

I don't think uncertainty in position and momentum are relativistically equal. However, if a non-relativistic assumption is to be made, then from Heisenberg's, and taking p=mv, then uncertainty in velocity>=(h/2pi)X(1/(uncertainty in position X mass)). Sorry for the math ambiguity. My device doesn't type LaTeX.

- 2 years, 1 month ago

Yes you are correct. You got the correct answer. Regarding the latex you can keep it in \ (...\ ).

- 2 years, 1 month ago

The LaTeX is not still working. It prevents me from posting some reeeeeeallly cool problems.;(

- 2 years, 1 month ago

$\text{Doubt : 4}$

In $(Si_4O_{12})^{8-}$, how many $Si - O - Si$ linkages are there ?

- 2 years, 1 month ago

I have an answer, but I am not totally sure it is correct. Coordination structure chemistry of silicates and silicones is my weakest point in chemistry. Perhaps I need to practise more!:)

- 2 years, 1 month ago

- 2 years, 1 month ago

It is 4.

- 2 years, 1 month ago

I was actually sure of 4 linkages, but I was not sure of one more. Thanks anyways.

- 2 years, 1 month ago

It's OK.

- 2 years, 1 month ago

You are a great guy, Ram.

- 2 years, 1 month ago

That's my quality quantitatively speaking.

- 2 years, 1 month ago

My goal in many interactions is to make them frictionless. Trivially speaking, I resist every enmity and conduct friendliness. I have even successfully transmuted people from an angry ground state, to a happy excited state!

- 2 years, 1 month ago

Oh !!! That's good.

- 2 years, 1 month ago

Thanks. Ask if you want more!

- 2 years, 1 month ago

Thanks guys. Keep sending problems and lets discuss!

- 2 years, 1 month ago

Hi guys! For sure we all have noticed that the derivative of kinetic energy is momentum. Is there a physical explanation for this?

- 2 years, 1 month ago

Quantitatively speaking, momentum is the product of mass of a body and its velocity. It is denoted by $\overline{P}$. $\large \overline{P} = m \overline{v}$ But the above definition is valid only when velocity of the body is constant. If the velocity of the body is variable we cannot use this formula and we should go by calculus. Physically speaking, momentum is the rate of change of kinetic energy with respect to its velocity. So, you ca say it as kinetic energy at that instance. Here is how we get $\overline{P} = m \overline{v}$ from kinetic energy. $K.E = \dfrac12 m (\overline{v})^2$ Now, differentiate both side with respect to velocity. We get : $\dfrac{d}{dx} K.E = \dfrac{d}{dx} \left ( \dfrac12 m (\overline{v})^2 \right )$ As, we know $\dfrac{d}{dx} K.E = \overline{P}$, we get : $\overline{P} = \dfrac12 \cdot m \cdot 2 \overline{v}$ So, we get : $\large \boxed{\color{#3D99F6} \overline{P} = m \overline{v}}$

- 2 years, 1 month ago

Perfect bro!

- 2 years, 1 month ago

Thanks. But what I should say you, brother or sister

- 2 years, 1 month ago

I am a young boy:)

- 2 years, 1 month ago

Ok

- 2 years, 1 month ago

Explain the Bohr theory of atoms, combining both mathematics and physics in your explanations.

- 2 years, 1 month ago

Does anyone know how to post a solution of a problem that doesn't have a posted solution yet?

- 2 years, 1 month ago

If you got it correct you click the button "No solution" under Continue and write. And if you got it wrong you can't.

- 2 years, 1 month ago

Thanks a lot, bro!

- 2 years, 1 month ago

You are welcome!

- 2 years, 1 month ago

@Mohmmad Farhan why can't you come here. I think this is a best place for a student like you. You can post your quires here.

- 2 years, 1 month ago

Sorry! I am not really active these days because of exams

- 2 years ago

Ok. No problem !!!

- 2 years ago

How do I post numerical answer problems on Brilliant?

- 2 years, 1 month ago

I think you have posted many problems in brilliant. However, when you are writng a question there will be two options, either Number or Multiple choice. You can select whatever you wish.

- 2 years, 1 month ago

Gearing up for today's 1st round olympiads!

- 2 years ago

Good luck!

- 2 years ago

Thanks. The results will be uploaded online in about 1.5 hours. Meanwhile I am posting them here for our consumption. Solve some, post solutions and invite others to do same!

- 2 years ago

Maybe you can post them like problems.

- 2 years ago

@B D Ok.

- 2 years ago

Problem 1: A password consists of $4$ distinct digits such that their sum is $19$ and exactly two of its digits are prime, e.g. $0397$. How many possible such passwords exist?

- 2 years ago

2,3: (2,3,6,8)

2,5: (2,5,4,8)

2,7: (2,7,4,6),(2,7,1,9)

3,5: x

3,7: (3,7,1,8),(3,7,0,9)

5,7: (5,7,1,6)

There are $7\times4!=168$ possibilities

- 2 years ago

How did you get all possibilities?

- 2 years ago

Find the 7 possibilities one by one, then times 24

- 2 years ago

Problem 2: What is the maximum possible area of a quadrilateral of sides $1, 4, 7, 8$?

- 2 years ago

I think we should use the concept of maxima and minima.

- 2 years ago

Perhaps you should solve it. I used the maximality condition of Bretschneider's formula. My answer was $18$.

- 2 years ago

Yes I too got like that.

- 2 years ago

What is that?

- 2 years ago

Looks similar to:

https://brilliant.org/problems/hexagon-octagon-in-a-rectangle/?ref_id=1538063

Maybe a harder version perhaps! :D

- 2 years ago

Problem 3: $20$ lines are drawn in a plane. What is the maximum number of parts into which the plane can be divided by the $20$ straight lines?

- 2 years ago

I think it is $211$

- 2 years ago

There is a trick. First, take the 20th triangular number. $\displaystyle\frac{20(20+1)}{2} = 210$ Add 1. $210+1=211$ These numbers are known as pizza numbers and are always one more than a triangular number.

P.S. @EKENE FRANKLIN did you use this method?

- 2 years ago

Great! Just what I wanted, and what I used during the examination!

- 2 years ago

Thumbs Up!

- 2 years ago

What is the remainder when $1^{241} + 2^{241} + 3^{241} + 4^{241}$ is divided by $5$?

- 2 years ago

$0$

- 2 years ago

Of course that is the answer, but prove it.

- 2 years ago

Since the divisibility rule of 5 only concerns the last digit, we have to find the last digits of the values. $1^{124}$ is obviously 1. Since the repetition in the last digit is (for 2): 2, 4, 8, 6 then $241 \div 4 = k (\text{Remainder}1$) the first number is 2 (in this set). Apply this to the other powers. Summing the last digits, we get 10 and $10 \div 5 = k (\text{Remainder}0)$

- 2 years ago

Excellent

- 2 years ago

Great job. I did modular arithmetic during the examination.

- 2 years ago

Me too

- 2 years ago

Problem 5: Find the general term of the sequence described by $a_n = 4a_{n - 1} - 3a_{n - 2}$ given that $a_1 = 1$ and $a_2 = 9$.

- 2 years ago

$a_n=4\times3^{n-1}-3$

- 2 years ago

Great. This was what I got. But do you mind showing your solution so I can clarify mine?

- 2 years ago

Solve the equation $x^2=4x-3$ and get $x=3$ or $1$. Let $b_n=3^n-1^n$.

The first few terms of $b_n$ is $2,8,26,80...$ and $b_n$ also satisfies the recursion $b_n=4b_{n-1}-3b_{n-2}$

Compare the two sequences: $a_n=\frac43b_n-\frac53=4\times3^{n-1}-3$

- 2 years ago

@X X Not exactly what I did, but something similar. Thanks a lot. If I may ask, have you ever participated in an olympiad before, or do you hope to participate in one?

- 2 years ago

No, I haven't. I knew few things about it, so I'm not sure about participating in one.

- 2 years ago

@X X Ok. Thanks. By the way, I really admire your problems. They are very cool. One of my major problems here is creating problems. My original problems are too easy(you can check them out). But solving others problems(of course not those extremely hard ones) is not a big problem for me.

- 2 years ago

@X X I think this is your first problem of the week in easy catogery.

- 2 years ago

You're right! (Ha, ha! I'm a little jealous of you because your problems are often the first problem in the easy category, and in your contributions page, the number of people are banging up:p)

- 2 years ago

@X X But I am not fully done. I expected that Number + Reciprocal will take me to 1 lakh (100 K) solvers. But it fell short of 7 K. But luckily this week too my question came in one of the problems of week (the first one) so it is confirmed that I will reach the milestone in one or two days.

- 2 years ago

@X X But some of your problems came in Intermediate and Advanced catogery.

- 2 years ago

I know. (Fewer people solves those, that is why I was so happy to see my problem as the second of the basic category)

- 2 years ago

@X X OH !!! Your problem is featured as the second one in the problems of the week. But my first problem (Thundering Question) is the third one.

- 2 years ago

Oh, I remember that one! (I loved that week because a lot of my solutions appeared in that week. )

- 2 years ago

@X X Yes, Vamprie Fan Club. It is were I had my first individual century. After that, the next week I had got 150 upvotes for my question Rising Balloons and the next week is a memorable for me, as I had my first double century for the question Counting 0's.

- 2 years ago

@X X Ram Mohith and X X, both of you are excellent problem contributors, some of the best here. I hope I can reach your level!

- 2 years ago

@X X It's a Fact :

I have made a hatrick in June 9 - June 29 (3 weeks) as 3 of my problem continuously came in easy part of the POTW. Now again the chance has come for me. Last week and this week too two of my problems are featured. So, if luck favors next week to I can have a problem in POTW. I am thinking very hard on which question should I post the next.

- 2 years ago

The sequel to the Mt Everest problem about pressure cookers?

- 2 years ago

- 2 years ago

Is it released yet?

- 2 years ago

No. Still under construction. Before that one I have two more questions, Raising Balloons - 2 and Popping balloons which are yet to be released. After these two the sequel for My. Everest vs Mt K 2 will be released.

- 2 years ago

OH!

- 2 years ago

How is my new problem, check it here. It is posed by B.D

- 2 years ago

Cool video!

- 2 years ago

@X X Yes. I liked that so much that I framed the question based on that.

- 2 years ago

@X X Don't worry mister !!! You have the skill to post and solve tough questions (level 4 and 5).

- 2 years ago

I made the cut for the 2nd round! I scored $76.70$ out of a maximum possible 110. Hurray!

- 2 years ago

Oh !!! Congrats.

- 2 years ago

Thanks a lot. But no one apart from us is solving the problems. I want to check my solutions and my faulty areas. Please direct the problem solving masters of Brilliant here to help me out.

- 2 years ago

If you want to direct anyone to this place just keep the symbol @ and type the name of the person. Immediately a notification will be sent to that particular user.

- 2 years ago

Hi guys !!! I want to tell you some secret. I think next week would be a week of physics. Because this week I have found six problems which have equal chances in coming to problems of the week. There are Rohit Gupta's Trick Spring Balance and Spring Balance, Pranshu Gaba's Three blocks Sliding and Relative Stuntmen Motion, Danielle Scarano's Thermographic Dog and my Mt. Everest vs Mt. Godwin Austin. I think these question will be featured definitely this week if not possible then next week.

- 2 years ago

@Calvin Lin

- 2 years ago

I think you there is some error in spelling or you have kept a gap between the symbol and name. Once check again. If it is correct then you should get it in blue color link and not just normal text.

For example you should type it as @ _ Ekene Franklin ( _ symbol means no gap) then you will get it as @EKENE FRANKLIN

- 2 years ago

It is not still working. Do I need to add something like a code or anything, or should I just type it?

- 2 years ago

You should select from the list which will appear when you type the name. Also the name should be exactly matching with that particular user even capital letters should be taken into consideration.

- 2 years ago

Which list?

- 2 years ago

Ok. If you want I will do it on behalf of you.

- 2 years ago

Of course I want! Thanks!

- 2 years ago

Tell the names of whom do you want to be called to this note.

- 2 years ago

@Calvin Lin, @Harsh Shrivastava, @Chew Seong Cheong, @Michael Mendrin, @X X, @Aniket Sanghi.

- 2 years ago

- 2 years ago

- 1 year, 10 months ago

@X X, @Michael Mendrin, @Chew-Seong Cheong, @Mohmmad Farhan,and the rest of all, Can you please participate in this message-board (as requested by Ekene Franklin)

- 2 years ago

What courses would you recommend for a 4th grader like me?

- 2 years ago

You are 4 the grade ????!!!!!

- 2 years ago

10 years old. I told you

- 2 years ago

But, I didn't think you are 4 th grade.

- 2 years ago

I am! REALLY

- 2 years ago

I am going to be 5th grade

- 2 years ago

Oh !!! Good. All the best

- 2 years ago

Actually I am 1 year away from board exam (in 2020)

- 2 years ago

My first trophy was in Grade 1(third)[english], Second in grade 2 (1st)[first scrabble competition] and third in grade 2(Best school player award)[first scrabble competiton]

- 2 years ago

BrilliantForLife

Dare you to toggle $\LaTeX$

- 2 years ago

I have a proof for the existence of infinite dimensions.

On a line (1 Dimension), a number can be represented by a point. On a grid (2 Dimensions), an intersection is represented for the data in a cell. In a cube (3 Dimensions), data can still be represented on a point (where straight lines intersect). Following this pattern, there are infinite dimensions (because there are $\aleph_0$ numbers).

- 2 years ago

Problem 6: Find all primes which are the sum of two primes and difference of two primes.

- 2 years ago

5=7-2=3+2,this is the only possibility.

- 2 years ago

Exactly. Just what I did during the exam, using the logic that if a prime satisfies those conditions, then the only even prime, 2 must be in the sum and difference.

- 2 years ago

Problem 7: Simplify $S = (cot 10^\circ - 3\sqrt{3})(cosec 20^\circ + 2cot 20^\circ)$

- 2 years ago

Why are you keeping square brackets. For square root you just need to keep flower brackets.

- 2 years ago

For trigonometric functions, logarithms, limts, etc you must keep a slash before them. Like \cot will be as $\cot$ and \log will be as $\log$.

- 2 years ago

Problem 8: A unit square is completely covered by $3$ identical circles. Find the smallest possible diameter of the circles.

- 2 years ago

Problem 9: How many $6$ digit numbers can be formed using only odd digits?

- 2 years ago

Is it 5^6?

- 2 years ago

Correct. Nice stuff. What did you do?

- 2 years ago

There are 1,3,5,7,9 five odd digits. There are six digits, each digit has 5 possibilities, so there are 5^6 possibilities

- 2 years ago

@X X Bro, u are amazing

- 2 years ago

DO YOU SERIOUSLY HAVE TO GIVE ME 46 NOTIFICATIONS OVERNIGHT!

- 2 years ago

Is that bad, Mohmmad? I am usually on Brilliant throughout the night.

- 2 years ago

I HAVE EXAMS

- 2 years ago

I see. But you can use Brilliant to prepare.

- 2 years ago

English EXAMS

- 2 years ago

Farhat, from which part of India are were from ?

- 2 years ago

- 2 years ago

I am also from Andhra Pradesh. From Visakhapatnam.

- 2 years ago

I am Telugu. You are Telugu right because you are from Andhra Pradesh right?

- 2 years ago

Yes. I am born in Visakhapatnam.

- 2 years ago

- 2 years ago

Sorry, but why?

- 2 years ago

See, My brother's name is Farhan but I am Farhat. And Mohmmad is his surname and Mohammad is my surname. (Stupid Passport errors)

- 2 years ago

- 2 years ago

YES! FINALLY!

- 2 years ago

You can change your name in the account settings

- 2 years ago

@X X I don't bother

- 2 years ago

Did you know that :

$1 + \omega = \omega \ but \ \omega + 1 \neq \omega$

Freakin' cool right?

P.S. $\displaystyle \omega \ is \ the \ second \ lowest \ level \ of \ \infty \ after \ \aleph_0$

- 2 years ago

Finally I reached it. I have reached 1 lakh (100 k) solvers in 91 problems.

- 2 years ago

Congratulations!

- 2 years ago

Do you know the minimum people to reach?

- 2 years ago

I didn't get your point !!! Are you asking about minimum people required to get contribution page.

- 2 years ago

Yes he is.

- 2 years ago

@X X I think you must minimum have 5K people reached. But the main parameter I think is that the contribution page is mostly obtained either by up votes or by solvers to the question (more than 1K). When I got my contribution page I have around 120 upvotes, around 300 solvers, around 30 views for my notes.

- 2 years ago

OK. Thanks!

- 2 years ago

@X X @X X, I want your help. I am trying to write a new problem but I got struck up at one point. Here is my doubt :

Suppose lets say a man jumps from a building with initial velocity $u$. After $x$ seconds another man freely falls from the same building and from the same height. Now, we can say that the displacement of both the man's are equal as they both reach the ground simultaneously after they jump from same point, so we can equate their distances. Here is what I did : $ut + \dfrac12 gt^2 = \dfrac12 g(t - x)^2$ where $t$ is the time taken by the first person to reach the ground. The main part of my doubt is that whether we should write the time taken by second person as $(t - x)$ or $(t + x)$.

- 2 years ago

I'm not good at physics, though. I think the time taken by the second person should be as same as the first one, maybe?

- 2 years ago

@X X What I think is that as the second person jumps after $x$ seconds his time period will be $(t - x)$ seconds. Let's ask it to staff.

- 2 years ago

So, are you caculating " when the first man fell to the ground, what is the distance between the two man"?

- 2 years ago

@X X No. Both man reach the ground simultaneously so can we write the equation as in my before comment in which we equate displacements.

- 2 years ago

Oh! Sorry, I misread the problem.

- 2 years ago

Yes, I too think the time taken by the second person is $t-x$

- 2 years ago

It should be t+x as he is free falling and the previous one jumped with velocity u

- 2 years ago

DO or DIE

You are lost in a forest on a cold midnight day. The temperature is quite low and it is bitter cold. Now you have only two chances :

• You should lie on the ground and should shrink your body like a tight pack.

• Go and stay in the water in a pond nearby.

There not much time left. Take your decision before cold kills you. So, what wold you choose ?

- 2 years ago

First option.

- 2 years ago

But the second one is the correct choice you have to make.

- 2 years ago

Why? Because of anomaly in expansion and contraction of water.?

- 2 years ago

And also due to the high specific heat capacity of water. This question is a slight modification of air currents (due to which it is cool during the day and warm during night near coastal areas) and I am going to post this very soon.

- 2 years ago

I thought as much.

- 2 years ago

Hello to everyone! I have not been around for some time now on Brilliant. However, I met on my return a delightful change in the method of posting options for multiple choice questions on Brilliant. Kudos to Calvin Lin and the truly brilliant Brilliant team!

- 2 years ago