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

  • Thread starter Thread starter 53Mark53
  • Start date Start date
  • Tags Tags
    Related rates
Click For Summary

Homework Help Overview

The problem involves a ladder leaning against a wall, with the bottom being pulled away at a constant speed. Participants are exploring how this movement affects the height of the ladder on the wall, specifically seeking to determine the rate at which the top of the ladder slides down.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the horizontal distance from the wall and the height of the ladder, questioning how to express the height as a function of the distance. There are attempts to apply the Pythagorean theorem and differentiate the resulting equations.

Discussion Status

Some participants have provided guidance on setting up the problem and differentiating the equations, while others are attempting to clarify the relevance of certain values and assumptions. Multiple interpretations of the setup are being explored, particularly regarding the height of the wall.

Contextual Notes

There is a mention of the direction being defined as positive upwards, and a specific speed at which the bottom of the ladder is moving away from the wall. The relevance of the calculated height of the wall is questioned, indicating potential confusion about the problem's requirements.

53Mark53
Messages
52
Reaction score
0

Homework Statement


laddercopy.png


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


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

The Attempt at a Solution


[/B]
this means that the wall height is 187.6 cm using pythagoras theorem

Any help will be much appreciated
 
Physics news on Phys.org
53Mark53 said:
does this mean when x=30 cm dx/dt = 25
Yes. Start with writing height of the ladder as a function of x.
 
cnh1995 said:
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
 
cnh1995 said:
Yes. Start with writing height of the ladder as a function of x.

I got the answer thanks :)
 
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.
 
53Mark53 said:
this means that the wall height is 187.6 cm using pythagoras theorem
The height of the wall is irrelevant to this problem.
 

Similar threads

Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 11 ·
Replies
11
Views
8K
  • · Replies 4 ·
Replies
4
Views
3K
Replies
2
Views
6K
Replies
6
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K