I was thinking in terms of direction, more than just speed; that’s why I specified vectors. Relative to the original vector, the first stage is deflected downward, the upper stage is directed downward.
I’d have to think about what the resultant speeds are. There’s no actual force pushing the two stages apart.
I’m not talking about thrust, I’m talking about the timing of the separation relative to how much the rocket has rotated.
The rocket is travelling, pointing along its velocity vector. At some point, it starts rotating (pitching up, in aircraft parlance). When it separates, the two pieces are going to start travelling in different directions. The new directions depend on when the separation happens.
How precise does that need to be, and how precise is the timing and operation of the clamps that hold the stages together? Suppose the clamps release a second too late, and the rocket has rotated a little farther than planned; the two stages will go in slightly different directions than planned. How much leeway is there in the pitch angle when the clamps release to still achieve the desired orbit?