Escape velocity from long ladder The escape velocity of earth is roughly $11 kms^{-1}$. However, what if a long ladder was built extending out of Earth's atmosphere and considerably more. Then if something was to climb up at much less than the escape velocity, what would happen when it reached the end?
And what if the object that climbed the "ladder" then fired some kind of thruster/rocket and was going fast enough so that it orbited the Earth. It would mean less energy required to get into orbit?
 A: "Escape velocity" is really just a measure of the kinetic energy an object near the surface of the Earth would need to have to start with in order to just run out of energy at the point where it was infinitely far from Earth, having converted all of its initial kinetic energy to gravitational potential energy.
Even if you built a giant ladder or a space elevator or whatever, the total energy required to get to orbit is exactly the same, it just comes in a less spectacular form. Rather than burning a rocket the whole way, you would be doing a slower conversion of energy into gravitational potential energy-- electricity running a motor to winch the rocket up to the top of a space elevator, or chemical energy from food as you climbed a bazillion stairs to get there, or whatever.
A space elevator would be an attractive way to get a rocket into orbit, or away from the Earth because it reduces the amount of rocket fuel you need to use to get there, replacing it with some other source that is more convenient (and less explosive) to work with. But you still need the same total amount of energy to get your payload into orbit.
A: If your ladder were the height of a geostationary orbit, which is about 6 times the radius of the Earth, then when you got to the end you could step off and be in orbit.  If it were lower, you would need to add energy to obtain a circular orbit.
The idea you're talking about is essentially a space elevator.  If it were feasible, it would be a far more efficient means of getting to orbit than chemical rockets.  Unfortunately, it is not feasible at this time for a variety of engineering reasons.
A: Energy required to escape from the earth's gravity is 
$\frac{GMm}{R} = mgR$
Now you may pay it in installments, you may pay it slowly but you may not pay less.
Escape velocity from point at height $h$ above the earth's surface is $V_{eh} = \sqrt{2g(R-h)}$.
Case I: Launching rocket from the surface of the earth i.e. h = 0
Total energy = Energy required to launch 
             = $\frac{mv_{e0}^2}{2} = \frac{2mg(R+0)}{2} = mgR $
Case II: Launching rocket from height $h$ above the surface of the earth
Total energy = Energy required to climb upto height $h$ + Energy required to launch
$mgh + \frac{mv_{eh}^2}{2} = mgh + \frac{2mg(R-h)}{2} = mgR$ 
A: Don't know how tall the ladder is, but it would get easier and easier to climb the ladder as you went up, because the gravititational force goes down as distance from the earth's center of mass increases.
If you're already up at some orbit height, you need only to thrust along your intended orbit until you reach the orbital velocity.  No need to thrust to get up to altitude since you're already there.
A: When you reach the end of the ladder you will fall back to earth, unless you have reached geo-synchronous orbit. Just compare the energy expended climbing with that required to reach orbit (which is more that the energy to just escape gravity vertically). If the ladder is longer than geo-synchronous orbit then you are no longer expending energy climbing, but on the contrary the earth is giving you energy. If you let go of the ladder you will fly out in space overcoming gravity.
A: Short answer: climbing such a ladder is acceleration. This is because the ladder is stuck into spinning earth, and you get higher speed by going up to higher radius. 
Regardless of spinning, escape velocity does depend on height. If you are static at infinity, you already have escaped.
