Results 1 to 1 of 1

Thread: Optimization - beam carried through hallways not horizontally

  1. #1
    Mar 2009

    Optimization - beam carried through hallways not horizontally


    Just wanting to check that I have taken the correct approach with this question. Its a two part question, the first part the standard longest rod/beam that can be carried horizontally through a hallway of $\displaystyle a$ meters by $\displaystyle b$ meters which is equal to:

    $\displaystyle L_{1} = l_{1} + l_{2}$
    $\displaystyle L = \left(a^{\frac{2}{3}}+b^{\frac{2}{3}}\right)^{\fra c{3}{2}} $
    Or $\displaystyle L = a\csc(\theta) + b\sec(\theta)$
    Where $\displaystyle \theta = \tan^{-1}\sqrt[3]{a/b}$

    The second part of the question which is the problem is... 'If the height of both hallways in part (a) is c metres and if the beam need not be
    carried horizontally, what is the length of longest beam that can be carried around the corner? [Hint: This is easy if you use the result of part (a).]

    My apprach is, to say you lay the rod/beam on the ground at point between the hallways that allows for the longest rod. If you then tilt the rod upward from one corner toward the ceiling you can 'draw' the rod (ie. the longest rod will go from the floor to the cieling at the point where the intial beam was the longest ie. it forms a right angled triangle), so to calculate this length is pythagoras theorem

    $\displaystyle L_{2} = \sqrt{L_{1}^2+c^2}$
    Attached Thumbnails Attached Thumbnails Optimization - beam carried through hallways not horizontally-untitled.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Strength Of A Beam
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Jun 11th 2009, 04:20 AM
  2. What is the weight of the beam?
    Posted in the Math Topics Forum
    Replies: 7
    Last Post: Jun 13th 2008, 02:49 AM
  3. Projectiles horizontally
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: May 19th 2008, 10:47 AM
  4. arrow problem, flying horizontally
    Posted in the Math Topics Forum
    Replies: 5
    Last Post: Nov 4th 2007, 02:28 AM

Search tags for this page

Click on a term to search for related topics.

Search Tags

/mathhelpforum @mathhelpforum