You are the stupid one here. Here is the proof that what i'm saying is true:
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If you read you can clearly see that Amaterasu is a short range attack
Also, even Amaterasu didn't directly appear where the person sees. Take a look here:
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If you analyse it you can see that it lands to the Raikage and because the Raikage dodged it, it continue his way to the samurai. So even Amaterasu isn't an instant jutsu.