Learn Finnish: Älä hyppää paniikissa, tai sinä hukut! - Do not jump in a panic, or you will drown!

The lesson is about verbs taking the illative (into) case. Neither hypätä nor hukkua has an illative word here, but do they normally take one?

Yes! If we added where you are jumping or drowning, Finnish uses the illative (mihin) case for both. Because drowning is seen as an irreversible process of ending up somewhere, you drown into the water (veteen) rather than in it (vedessä), just like you leave or forget things into a place.

Why is it hyppää instead of hypää, since the basic verb is hypätä?

The verb hypätä (to jump) is a type 4 verb. To form the negative imperative (älä hyppää), you use the present tense stem. Type 4 verbs undergo reverse consonant gradation (weak to strong) when conjugated, so the weak single p in the dictionary form becomes a strong double pp in the stem.

Why does hukut have only one k when the dictionary form is hukkua?

Hukkua (to drown) is a type 1 verb. When you add the -t ending for you (sinä), it closes the final syllable. A closed syllable triggers standard consonant gradation, softening the strong double kk to a weak single k.

Why is it paniikissa (in a panic)? Is that a location?