Answer:
The word vigorous affects the meaning of the sentence by making it clear that the one that says I know, instead of I think is considered as a person who has a strong will and personality.
Step-by-step explanation:
The word vigorous describes something strong, something energetic and forceful; that is why it affects the sentence by expressing how determined is a pilot who uses the phrase I know. How decided he is and how strong will he has, how vigorous he is. On the other hand, these lines also show with what scorn a pilot was looked upon if he ever ventured to say I think. This phrase (I think), in contrast with I know, is a weak phrase which is supposed to transmit insecurities and weak will.