Take a look at this...
For the above nuclear ICBM, each warhead is actually smaller than a man.
The DF-21 is purportedly a single warhead missile. If the warhead is to be maneuverable, even if it is a single event maneuverable, meaning because of its high descent speed, it has time to execute only one attitude change, the warhead would still need some internal space to accommodate the necessary hardware for it. So whatever 'payload' specs that are in the public domain -- discard them. To truly disable the ship, not necessarily sink it, to remove it from the mission, the impact would have to be spot on the middle of the deck. The explosion would have to be a few microseconds from impact fused to maximize below deck damages.
The main technical hurdle will be the sensor package. Assuming radar for now, the warhead will most likely have as narrow a nosecone as above, which will limit its radar antenna, which will limit its view, which will make it vulnerable to countermeasures, specifically radar view saturation. Yes...I read your source on how far a carrier can maneuver with the time alloted but like I said before, in a ship versus missile engagement, if the missile or warhead failed by one meter, the ship win. All the carrier and its escorts has to do is deploy whatever countermeasures combinations and sharp maneuvers to cause that failure. In a single attack, there will be more countermeasures available than there could be missiles launched.
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It is safer to assume that the threat coming from the missile is of a signifcant threat. The China we have now is not the China of 50 years ago. They are able to put a man in space, build a 5th gen fighter, launch satelites into orbit therefore it is naive to think that this is beyond their capability.
I find it extremely difficult that the hurdles associated with targeting a ship with a ballistic missile have been overcome.
The reaction times are tiny, the onboard space is tiny, the target is tiny, the forces are enormous.
hard
In real war scenario, it is unlikely that this will be the only thing launched at the carrier and the rest be on standby and wait fot it to hit the carrier before unleashing their next string of actions. This could be served as a distraction to open up an attack or together with air and naval assault. The battle group will have to deal with multiple threat coming at them at the same time.