Are you suggesting that a free fall of, say, 4 minutes and 36 seconds is not possible?

4 minutes and 36 seconds?

So 276 s, with a constant acceleration of 9.8 m/s^2? (assuming suborbital flight in the atmosphere).

Best case scenario, starting at a high vertical speed, going up to the peak at 138 s in, and then falling back down.

That puts the speed at the start (and end) as 1352.4 m/s or roughly 1 km/s.

That is between mach 3 and 4.

That alone makes it basically impossible to do other than as an orbit.

You would need some of the fastest planes available which are not large enough for the scenes.

But lets ignore that for now.

If you started at ground level, you would reach a peak of 0.5*9.8*138^2 m. That is 93315.6 m, or roughly 93 km. The "official" definition of space is 100 km.

So in order to not crash into Earth and not go to space, you have 6684.4 m to lose 1352.4 m/s after your descent (and similarly before your ascent). We can find the acceleration required similar to the above.

You have a=a;

v=v0+a*t;

d=d0+v0*t+0.5*a*t^2.

Noting that at the end (t=te), v=0 and d=0.

Thus v=0=v0+a*te

a=-v0/te

v=0=d0+vo*te+0.5*(-v0/te)*te^2

=d0+v0*te-0.5*v0*te

=d0+0.5*v0*te.

te=-2*d0/v0

Noting that d0=6684.4 m and v0=-1352.4 m/s

This gives us te=2*6684.4 s / 1352.4.

So that gives 9.885... s.

I'll be nice and call it 10 s.

So we have 10 s to lose 1352.4 m/s.

That means we need an acceleration of 135.24 m/s^2.

That is ~ 14 g. Well past lethal, especially when sustained for 10 s.

This is also how fast it needs to go up.

I don't know of any vehicle that can do that.

So it seems the only way to do it is to go to space.