Manhole cover thought to be propelled into space

Forces would be different all over the surface. Assume for a moment that it launches straight up and does not translate, that is, remains "flat", perfectly parallel with the plane of its launch point.

There would be reduced force on the bottom and considerable force on the top, just from air pressure. Hold your hand out the window at 100km/h to learn what I mean: The forward side of your hand faces increased air pressure, the backward side has reduced air pressure.

So far, so good. Now add the vortices curling around the edges of this flat object - there will be force differentials.

Now add the vortices on the forward surface: Unless this object is optically flat, it will have sufficient surface features to create all manner of weird fluid dynamics, if traveling at the suggested speed.

Will it deform? Hmm, good question. First thing that will happen is wicked random translation (pitch and roll) due to the differences in force described above.

If it doesn't make orbit, it might deform under heat stress on the way down. The way up it would probably travel like a knuckleball, but on the way down it might start to stabilize.

I'm not what the odds are, but my guess is the two most probable descent motions are, one, knife edge descent, in which case the leading edge heats up, and it starts to soften and deform, and two, spin about a lateral axis parallel to the earth. In this latter case, I don't know if there would be enough heat on the two "leading edges" to cause deformation (think of it coming out of clock, spinning clockwise: as each edge passes noon, it hits "harder air" as it passes down to 6).

If it continues in knuckleball descent, I should think heat buildup would be evenly dispersed.

Deformation would occur if sufficient heat builds up to soften the metal.

Note: if the object isn't metal, or is mixed metal and other material, it's likely that it would break apart due to either or both of uneven heat distribution and uneven resistance to force differences. Or combust.

Objects behave weirdly when traveling that fast in dense fluids.

As Peter (sibling) mentioned, the force would not be equal across the surface. If it was propelled straight (i.e. orthogonal to the radius of the Earth), then there'd be some serious eddy effects of airflow around the circular edge (cross-section).

Probably the best thing that could happen from a NOT-deform standpoint would be to have it launched at an angle, i.e. as if a quarter fell on the Earth and landed on it's side (neither face). This would present the smallest and most uniform cross-section possible (as opposed to the face of the quarter looking into space, the rim/edge of the quarter points up skyward).

Also air resistance is extremely tricky at "normal" speeds, let alone at 10km/s+, and I think the real factor would be the currents of air around the edges, massive turbulence = massive amounts of friction/heat on the edges. It would be a mess! Hopefully that makes it a little clearer :)