Ladder Question

[johnjones]

I don't understand the question, as in what it is trying to ask:

What is the path traced out by the middle rung of the ladder (10 ft. long) sliding down the wall?

Once I understand what I'm being asked to find or what to do, I might have an idea to do it. Can someone kindly guide me thro' this? Thanks so much.

 

[Gene]

It starts out staight up. The middle is at P(0,5). It ends up at P(5,0). It goes thru P(5/sqrt(2),5/sqrt(2)) half way down.
You want an equation that will make the center go thru those points as the bottom goes from P(0,0) to P(0,10)

 

[Gene]

You didn't "come back" but I decided my hint was vague so...

The center of the ladder is at P(x,y)
x is half way between the wall and the bottom of the ladder.
y is half way between the ground and the top of the ladder.
The ladder is 10' so
(2x)² + (2y)² = 10²
You should recognize that equation and the path should be obvious.

 

[johnjones]

It starts out staight up. The middle is at P(0,5). It ends up at P(5,0). It goes thru P(5/sqrt(2),5/sqrt(2)) half way down.
You want an equation that will make the center go thru those points as the bottom goes from P(0,0) to P(0,10)

I am having a hard time picturing this, starting out straight up. I understand your technique, but I don't even know what it is asking me to do or find. Any possible way you can reword the question? Thanks so much, Gene.

 

[Gene]

It starts out standing straight up against the wall. Just go against your arrows till the bottom is at the wall and the top is 10' high and against the wall. That is the starting position. Then as the bottom is pulled away from the wall it looks like your picture untill it is flat against the ground. They want the equation for where the center of the ladder is as the bottom moves.

 

[johnjones]

You didn't "come back" but I decided my hint was vague so...

The center of the ladder is at P(x,y)
x is half way between the wall and the bottom of the ladder.
y is half way between the ground and the top of the ladder.
The ladder is 10' so
(2x)² + (2y)² = 10²
You should recognize that equation and the path should be obvious.

I don't recognize this equation . I understood the method, but am I now trying to find x or y. Do I use pythagoras?

 

[Gene]

You have to learn to recognize a some equations. One is the circle, x²+y²=r²
Just simplify
(2x)² + (2y)² = 10²
and that's what you get. A circle of radius 5.