Man Ladder
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Man Ladder
Don't Blame the Ladder – Ladder accidents are often not the ladder's fault
Ladder accidents are a frequent occurrence. Every year thousands of people are injured using ladders at home or in the workplace. Ladder accidents are now so common many trades and industries are forgoing them and turning to other methods of working at height – despite these methods being more time consuming, expensive and less practical.
However, there are several reasons for this high number of accidents involving ladders, but the ladder itself is not to blame and there is no reason why you shouldn't buy a ladder for working at height.
Ladders are safe is used correctly
Firstly, there are a high number of accidents involving ladders, not because they are a dangerous item, but because working at height is dangerous full stop. Regardless of how you get up there, if you have a fall from height there is more risk of injury or death.
Secondly, ladders, despite their safety record are an incredibly common tool still used all over the place. They are by far the simplest, easiest and most convenient method of working at height which is whey there are nearly as many ladders on the planet as there are people. Because ladders and ladder use is so common it stands to reason that there are a high number of accidents involved with using ladders.
Thirdly, when a tool or piece of equipment is used incorrectly, you can hardly blame it for any mishap in its use. And this is as it is with ladders. Improper use, or the use of the wrong type of ladder will often lead to accidents.
Take this example from a newspaper a few weeks ago where a handyman fell from a tree after he sawed off a branch that he had leaned his ladder against . He had rested the tree on the branch, climbed up then proceeded to saw through it. Once the the branch was sawn through, it, along with the handyman, ladder and saw – all plummeted to the ground.
Thankfully the man wasn't injured but it is a good demonstration of how ladder accidents often occur through lack of thought or pre-planning. When using a ladder its important to asses what type of ladder you will need, where it will be placed and to identify any potential hazards. If used correctly, good quality ladders are no more or no less dangerous than any other tool
About the Author
Richard N Williams is interested in ladders, extension ladders and step ladders. Please visit us website if you are interested in buying a ladder or need advice about ladders
(Derivative problem) - A man left a ladder of length L leaning against the side of a palace...?
A man left a ladder of length L leaning against the side of a palace, and it started to slide. The bottom of the ladder slid along the ground with a constant speed of u meters/sec.
How fast was the top of the ladder sliding down the wall?
Why do I have to use derivative? Can someone explain to me how you do it and why you did it?
This is called a "related rates" problem, and you use derivatives with respect to time (t) because rates are changes with respect to time.
Let's say X is the distance from the base of the palace wall to the base of the ladder, and Y is the distance from the base of the palace wall to the top of the ladder. The only information you're given is that dx/dt = u, and you are being asked to find dY/dt.
By Pythagorean theorem, we have this relationship:
X² + Y² = L²
X and Y are changing, L is not, so you can consider L just a number, not a variable.
Differentiate implicitly with respect to time:
2X (dx/dt) + 2Y (dy/dt) = 0
X (dx/dt) = -Y (dy/dt)
Xu = -Y (dy/dt)
Therefore, dy/dt = Xu/-Y
"The Man on the Ladder": 40 Years of Dr. Arthur C. Bartner and The Spirit of Troy