Gosh mister, I sure hope they are smart enough to do the boom in front of the incoming missile rather than after they pass each other.
Perhaps you should tell them?
No, the rocket scientists told me already (I was basically quoting them overcoming my ignorance), they know there are issues.
What this all means is you cannot take an ABM (air breathing Missile such as a Patriot missile) to take out an ICBM.
Now you want more fun, get into curvature of the earth versus radar coverage then including intercept times. Note that the intercept missile is not in space waiting to engage, it is covering the projected point of impact. Which means it is earth based and has to be launched after the ICBM.
Gosh mister, an ICBM is launched, at what point of its flight path do we know where it is targeted to impact? Try to get within 100 miles for a point of impact. (let's ignore MIRVs for this response).
Can you say after it is on its downward path? So how much time does a land based missile intercepter have to engage to prevent damage to the target? Gosh mister, I hope you are smart enought to provide the data to stop this attack.