Can I say "dived" instead of "jumped" in this context?
Yes, they imply the same action here! You can use "dove" (past tense form of "dive") instead of "jumped" here. Note that to "dive into/right in" is an informal expression meaning to "do" or "start" something with enthusiasm! You might see it used occasionally. Ex: The lifeguard dove into the water to save a little boy. Ex: After purchasing the book, I dove right in. Ex: I dove into my pasta. It was delicious.
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