It is just how we are taught about Escape Velocity. Look at this page from Georgia State:
http://hyperphysics.phy-astr.gsu.edu/hbase/vesc.html
Yes, look at what it actually says, not what you want to pretend it says:
If the kinetic energy of an object launched from the Earth were equal in magnitude to the potential energy, then in the absence of friction resistance it could escape from the Earth.
Notice how it appeals to the kinetic energy rather than velocity in a particular direction?
You can go straight up, but you don't need to.
If you go at an angle away from straight up, but still at escape velocity, you still escape, after following part of a hyperbolic orbit.
This is because you have enough kinetic energy to escape the gravitational potential well.
The only way you wont escape is if you do something to lose speed other than gravitationally interact with the planet, for example, firing rockets to slow down or crashing into the planet.
Just what source do you know of which claims you must be going straight up right from the start to escape?
Just what do you think would happen if an object went at 100 000 km/hr at an altitude of 1000 km above Earth's surface, in a direction 90 degrees from straight up?
If you put in 1 and 1.1 for the Mass and Radius
Then you are dealing with an altitude of ~637 km.
According to this:
https://www.hq.nasa.gov/alsj/a11/a11fltpln_final_reformat.pdfThe initial orbit was 100 nautical miles (I am assuming that is what they meant rather than nano meters), or 185.2 km.
That puts it at 1.029 Earth radii.
That results in an escape velocity of ~24 650 archaic units per hour.
Put if they reached it or not is quite irrelevant.
They didn't just coast from then on. They had more burns which affected their velocity.
Your own source contradicts you. The image you shared with us says that it's in relation from the body center of mass.
No, his source fully supports him.
It clearly states that the direction does not matter.
What is in relation to the body's centre of mass is the distance.
The escape velocity is dependent upon the gravitational potential energy, and thus on the distance to the centre of mass of the body.
So distance is from the centre of mass, not direction, as direction does not matter.