How Fast is the Top of the Ladder Sliding Down When the Bottom Moves Away?

[53Mark53]

Homework Statement

A 1.9 metre ladder is leaning against a vertical wall. If the bottom of the ladder is 30 cm from the wall and is being pull away from the wall with a horizontal speed of 25 cm per second, how fast is the top of the ladder sliding down the vertical wall?

We define the the direction up the wall to be positive, so that your answer must be negative.

Homework Equations

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does this mean when x=30 cm dx/dt = 25

The Attempt at a Solution

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this means that the wall height is 187.6 cm using pythagoras theorem

Any help will be much appreciated

 

[cnh1995]

does this mean when x=30 cm dx/dt = 25

Yes. Start with writing height of the ladder as a function of x.

 

[53Mark53]

Yes. Start with writing height of the ladder as a function of x.

does this mean

h=x^2+y^2

dx/dt=2x+2y

25=2x30+2y
-35=2y
y=-17.5

 

[53Mark53]

Yes. Start with writing height of the ladder as a function of x.

I got the answer thanks :)

 

[cnh1995]

Height of the ladder is h=√(L²-x²), where L=length of the ladder i.e. 1.9m.
You can proceed by taking derivative on both sides w.r.t. time.

 

[Mark44]

this means that the wall height is 187.6 cm using pythagoras theorem

The height of the wall is irrelevant to this problem.