Placing rock under ladder to stop it from slipping

[ChiralSuperfields]

Homework Statement

Please see below

Relevant Equations

Please see below

For part(a) and (b),

The solution is,

Can someone please explain the solutions to (a) and (b) to me? I don't understand where they got 5.77 cm from.

Many thanks!

 

[hmmm27]

They used b to get a.

What answer did you get ?

 

[ChiralSuperfields]

They used b to get a.

What answer did you get ?

Thanks for your reply @hmmm27 ! The got 5.77 cm. But don't you think that is a little strange using (b) to get (a)?

I still don't understand (b). Many thanks!

 

[hmmm27]

So, what answer did you get ? and how did you arrive at it.

 

[ChiralSuperfields]

So, what answer did you get ? and how did you arrive at it.

I did't get an answer @hmmm27. I am wondering how the solutions arrived at their anwser.

 

[haruspex]

is a little strange using (b) to get (a)?

Not at all. The answer to part b) is the explanation of how they arrived at the solution to a). Presumably this uses ideas earlier in the chapter, but I do not have the book.
Draw a diagram showing the ladder in both positions. Label the right-hand foot of the ladder P (the pivot point), the right-hand top of the tilted ladder B, the right-hand top of the upright ladder B', the left-hand bottom of the tilted ladder A, the left-hand bottom of the upright ladder A'.
Drop a vertical from A' to meet the sloping ground.
Draw a horizontal from B to meet PB'.
Spot similar triangles.

 

[ChiralSuperfields]

Not at all. The answer to part b) is the explanation of how they arrived at the solution to a). Presumably this uses ideas earlier in the chapter, but I do not have the book.
Draw a diagram showing the ladder in both positions. Label the right-hand foot of the ladder P (the pivot point), the right-hand top of the tilted ladder B, the right-hand top of the upright ladder B', the left-hand bottom of the tilted ladder A, the left-hand bottom of the upright ladder A'.
Drop a vertical from A' to meet the sloping ground.
Draw a horizontal from B to meet PB'.
Spot similar triangles.

Thank you @haruspex , I will try that!

 

[Lnewqban]

Can someone please explain the solutions to (a) and (b) to me? I don't understand where they got 5.77 cm from.

Many thanks!

I don’t see a reason for translating tilting into angle and back to vertical displacement of the left leg.
Are you familiar with similar triangles?

https://www.mathsisfun.com/geometry/triangles-similar.html

If so, I would draw a 0.41 x 0.41 square at the bottom of the rectangle formed by the ladder dimensions.
The horizontal displacement of the top corners of that square should be equal to the vertical one, and both should be proportional to the horizontal displacement of the top of the ladder.

 

[ChiralSuperfields]

I don’t see a reason for translating tilting into angle and back to vertical displacement of the left leg.
Are you familiar with similar triangles?

https://www.mathsisfun.com/geometry/triangles-similar.html

If so, I would draw a 0.41 x 0.41 square at the bottom of the rectangle formed by the ladder dimensions.
The horizontal displacement of the top corners of that square should be equal to the vertical one, and both should be proportional to the horizontal displacement of the top of the ladder.

Thank you for your reply @Lnewqban ! Yeah I'm familiar with similar triangles.

 

[Lnewqban]

Thank you for your reply @Lnewqban ! Yeah I'm familiar with similar triangles.

You are welcome.
Then, you now understand where they got 5.77 cm from.

We have two triangles that are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Please, see scaled drawing representing our problematic ladder.

 

[ChiralSuperfields]

You are welcome.
Then, you now understand where they got 5.77 cm from.

We have two triangles that are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Please, see scaled drawing representing our problematic ladder.

That is very helpful @Lnewqban ! Thank you for your help!