I have tried doing the fol. A corridor 4 ft wide opens into a room 100 ft long and 32 ft wide, at the middle of one side For my version, however, because our length is determined by considering the maximum horizontal displacement at the hallway width $b$, we can be certain that if we try to move the ladder through translation + rotation, no impingement will occur.
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When $x \in [0, l]$ the rod has to be tilted upwards by an angle $\theta$ for the rod to be able to pass through
The part i'm especially unsure about is
Let's tilt the rod so that is touches the upper point of the doorway (as shown in the image). I want to fit a 82x39x24 inch (hxdxw) shaped object through a 79 inch tall door frame, how can i calculate the angle of tilt needed to fit it through the frame? The problem asks for the length of the longest rod that can be placed in a rectangular room with given dimensions What is the maximum length of a rod which can be kept in a rectangular bo.
Not the question you're searching for Geometry, pythagorean theorem, 3d distance To find the maximum length of a rod that can fit inside a rectangular box, we need to calculate the space diagonal of the box. It is one interpretation of the term length, but i wouldn't assume that it must hold
In any case, even if i do know that breadth is less than 6, it could be 1 or 2 or 5 etc.
My professor walked us through how to derive a formula for the maximum possible length of the pipe, ultimately arriving at the equation $l = (a^ {2/3} + b^ {2/3})^ {3/2}$ The issue i have is understanding intuitively why this formula works, and exactly what it's doing. The idea is how to determine if it is possible to move a rectangular 3d box through the corner of a hallway knowing the dimensions of all the objects given Consider a hallway with width $1.5$ and height $2.5$ which has a corner of $90^\circ$.
