| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 979.1 | | BEING::POSTPISCHIL | Always mount a scratch monkey. | Mon Nov 28 1988 18:01 | 23 |
| Re .0:
Consider two points, one the corner and one the point where the ladder
touches the other side of the 8 foot passage. Our initial condition
has one end of the ladder at the corner and the other at its farthest
down the 8 foot passage. The angle from the ladder to the wall is O,
where O = arc sin(8/29).
As we move the ladder up the passage, a bit of it sticks out. Now the
portion of the ladder still in the 8 foot passage is the hypotenuse of
a right triangle, where O is another angle and the length of the
opposite leg is 8 feet. So the length of that portion of the ladder is
8 / sin(O). The length of the rest of the ladder is 29 - 8/sin(O).
The horizontal amount by which that rest of the ladder sticks out
beyond the corner is cos(O) * (29-8/sin(O)).
Take the derivative of that, solve for a zero value between arc
sin(8/29) and a right angle, and put the result back in the above
formula. The length is about 12.685.
-- edp
|
| 979.2 | 29? | KIRKWD::FRIEDMAN | | Mon Nov 28 1988 22:26 | 2 |
| Where does the "29" come from? Could you mean "27" in all those
expressions?
|
| 979.3 | | BEING::POSTPISCHIL | Always mount a scratch monkey. | Tue Nov 29 1988 12:06 | 6 |
| Re .2:
Yes, they should all be 27, which changes the answer to about 11.18.
-- edp
|
| 979.4 | 5**1.5 | CLT::GILBERT | Multiple inheritence happens | Tue Nov 29 1988 13:48 | 87 |
| 979.5 | | CLT::GILBERT | Multiple inheritence happens | Tue Nov 29 1988 17:03 | 6 |
| > 2/3 3/2
> x = - w ( (l/w) - 1 ) . (a pretty result)
Even nicer:
2/3 2/3 3/2
x = - ( l - w ) .
|
| 979.6 | Moving sofas | AKQJ10::YARBROUGH | I prefer Pi | Tue Nov 29 1988 18:38 | 10 |
| Here's a related problem that is somewhat easier to solve:
A building has two hallways meeting at right angles, each 6 feet wide. If all
sofas are 3 feet wide, what's the longest sofa that can be moved from one
hallway to the other (while being kept level)?
In this version you can take advantage of symettry to simplify the
solution. Only quadratics are involved.
Lynn Yarbrough
|
| 979.7 | 3-D | AITG::DERAMO | Daniel V. {AITG,ZFC}:: D'Eramo | Tue Nov 29 1988 21:15 | 5 |
| re .6
How high is the ceiling?
Dan
|
| 979.8 | but the cushions will fall out | AKQJ10::YARBROUGH | I prefer Pi | Wed Nov 30 1988 14:15 | 7 |
| No, no, I said *level*. No fair tipping it.
Actually, the length of sofa in this problem actually exceeds the height of
most ceilings (8 ft.) but let's leave the 3-d case as an exercise for the
ambitious reader.
Lynn
|