Recent content by brotherbobby

  1. brotherbobby

    Two balls, dropped with a delay of ##\Delta t##, meet after rebound

    I have drawn a figure of what I meant to the right. A ball is projected vertically from a point A on the ground with a velocity ##v_0##. It travels to a maximum point B at a height ##h## from the ground and falls back to the ground. Imagine a point C intermediate between A and B at a height of...
  2. brotherbobby

    Great circle between two points on the Earth's surface

    Sorry for coming in late. I would use the method you proposed @kuruman presently, but please tell me if there's something wrong with my solution above. (Post #1) I think it would be better if I put the problem statement again. Of course it's crucial what I am assuming as "co-ordinates of the...
  3. brotherbobby

    Two balls, dropped with a delay of ##\Delta t##, meet after rebound

    I had asked at @A.T. : ``Is it also true that for a ball thrown vertically up and which rises to a maximum height ##h##, the time to scale a height ##y## is the same as the time that the ball dropped from the height ##h## will take to fall a distance ##y## down?" What I meant was, if the ball...
  4. brotherbobby

    Investigating the real roots of a cubic equation

    I copy and paste the problem to the right of the screen. Please look at part (c) where, we believe, the error has taken place in what we are seeking to prove. This is the book, complete with its author(s) and edition : Riley, K.F.; Hobson,M.P.; Bence,S.J. (2006) Mathematical Methods for...
  5. brotherbobby

    Investigating the real roots of a cubic equation

    When you type your problem statement and relavant equations, you have to include actual equations in LaTeX. Your problem statement may contain an equation. As for relevant equations, it goes without saying that you may have an entire list of them numbered from 1 to ##n##. Sometimes, I even...
  6. brotherbobby

    Investigating the real roots of a cubic equation

    Yes. Upon edit, only if it's the opening post (#1) of the thread, the ##\rm{\LaTeX}## codes disappear. What I do is to open an older page of the post and rewrite the equations again in the new page. But of course it's a lot of work all over again. And each time you edit your thread opening...
  7. brotherbobby

    Great circle between two points on the Earth's surface

    Problem statement : I copy and paste the problem as it appeared in the text. [Kleppner, D., Kolenkow, R. (2014). An Introduction to Mechanics. Cambridge University Press (2E)]. The statement itself is rather long-winded. The question to be answered appeared towards the end of the passage ...
  8. brotherbobby

    Investigating the real roots of a cubic equation

    None of the codes in the Relevant Equations show. It is my mistake too that when I decided to edit my original message that starts the thread (#1), I edited only the "body" of the message, without looking at the title or the Relevant Equations, or the Problem Statement. Anything written in...
  9. brotherbobby

    Investigating the real roots of a cubic equation

    The ##\rm{\LaTeX}## renders but is cleaned upon an edit. You have to type all LaTeX codes again.
  10. brotherbobby

    Investigating the real roots of a cubic equation

    Thank you @Ibix. I should add, to help the admin, @Greg Bernhardt, that the formatting in ##\rm{\LaTeX}## does not disappear in the main text, where we type in our attempt and doubts, if we try to edit our message. Needless to say, this is also not a problem in all future replies. But for the...
  11. brotherbobby

    Investigating the real roots of a cubic equation

    Hi @pasmith, yes it seems I was mistaken too in my plotting on ##\verb|desmos.com|##. I took the constant ##k## with a positive ##(+)## sign. Of importance is the minus ''##-##'' sign before the term ##k## in the question, as you pointed out. If it was ##+k##, then the book is correct. As it...
  12. brotherbobby

    Investigating the real roots of a cubic equation

    Statement of the problem : Let me copy and paste the problem as it appears in the text. [Riley, K.F., Hobson,M.P., Bence,S.J. (2006) Mathematical Methods for Physics and Engineering. (3E)]. Attempt : One real root is guaranteed, as ##n =\;\text{odd}##. Differentiating ##f'(x) =...
  13. brotherbobby

    Undergrad Textbook description of R##\ddot{\text o}##mer's light speed calculation

    Yes sorry about that. I agree. I am sorry I don't see how that is - the earth's motion, whether towards or away, affecting when the earth sees the moon disappear and reappear. I am sure it won't be easy for you to draw a diagram for it. Do you have a text with a diagram to which I can refer...
  14. brotherbobby

    Undergrad Textbook description of R##\ddot{\text o}##mer's light speed calculation

    Let's have the image again. It might be obvious from the picture, but let me state it all the same. In 1 and 2, the object it moving away from Jupiter, while in 3 and 4, it is moving towards. In 1 and 3, the moon Io is seen by the earth to be sliding out of the eclipse, while in 2 and 4 it is...