Ballistics is a well-understood science. Computers make it easy, not just calculating the intercept but refining it as the distance closes. The closer the merging rockets get, the greater the accuracy.
Apparently you don’t understand how _fast_ computers run today. The one you are using RIGHT NOW is SO FAST that in the time that it takes _light_ to go from the screen to your eyes, your computer has carried out at least 4 instructions; in the flight time for ID missile, it can carry out literally billions of instructions.
“Doesn’t have much time”? meh, the ID onboard computers are _bored_ during most of the process.
I know how fast computers run.
seconds count when trying to intercept a missile.