[hermitcrab]

>It's quite easy, using a jet aircraft, to (via a ballistic trajectory) get into space

A jet engine requires atmosphere. Spaces requires no (or very little) atmosphere.

The edge of space is usually defined at 100km (the Karman line).

The highest altitude reach by an air breathing jet is around 37km. https://en.wikipedia.org/wiki/Flight_altitude_record

A scramjet might get to ~75km according to: https://aviation.stackexchange.com/questions/44837/what-is-t...

[wizzwizz4]

That's the point at which the jet stops working, but by that point you can be going quite fast. If there isn't enough air to run the jet engine, there also isn't enough air to slow you down (much).

[hermitcrab]

Assuming no air resistance and 10m/s^2 gravity. I calculate that you would have to be doing ~1,100m/s (~mach 3.2 at sea level) straight up at 37km to reach 100km. Or ~1,600m/s (~mach 4.7 at sea level) at 45 degrees to perpendicular.

[wizzwizz4]

Seems about right. https://en.wikipedia.org/wiki/Project_HARP (1966) got 2100m/s from a ground-based cannon: this got the projectile to 179km.