Minimization Problem

[JSmith]

A fence is 1.5 m high and is 1 m from a wall.
A ladder must start from the ground, touch the top of the fence, and rest somewhere on the wall.
Find the minimum length of such a ladder.

The distance from the bottom of the ladder to the start of the fence is

So the length L of the ladder is

or

Taking derivatives gives you:

Setting to 0 and solving gives you

I get 3.5117 m with angle between ladder and ground ~0.8528 radians

Book says my answer should be ~4.5...

 

[mmm4444bot]

The sun is finally shining in San Diego, today, so I'm off to the Silver Strand (for a nice bike ride).

I just did some quick scratch work, using a different approach, and I arrived at the same result as you did.

Maybe we both made similar logic errors. Or, maybe your book's answer is wrong.

Let's wait for somebody else here to give it a go...

 

[Deleted member 4993]

A fence is 1.5 m high and is 1 m from a wall.
A ladder must start from the ground, touch the top of the fence, and rest somewhere on the wall.
Find the minimum length of such a ladder.

The distance from the bottom of the ladder to the start of the fence is

So the length L of the ladder is

or

Taking derivatives gives you:

Setting to 0 and solving gives you

I get 3.5117 m with angle between ladder and ground ~0.8528 radians

Book says my answer should be ~4.5...

I got the same result as you did..