Breakdown of Kötturinn hoppar upp á þakið.
kötturinn
the cat
á
onto / on / in (static location) / on (a day of the week)
upp
up
hoppa
to jump (hop)
Questions & Answers about Kötturinn hoppar upp á þakið.
Why do we use upp here instead of uppi?
Because the cat is moving to a new location. We use upp (upwards) for motion towards a place, and uppi (up) when something is already stationed there. Since the cat is jumping onto the roof, it is an action with a destination.
Why does the preposition á trigger the accusative case for þakið (the roof) here?
The preposition á takes the accusative case when it describes movement towards a new destination. If the cat were already on the roof and just jumping up and down in the exact same spot, we would use the dative case (á þakinu).
Wait, doesn't the nominative (subject) case of 'the roof' also look exactly like þakið?
Yes! The word þak is a neuter noun, and neuter nouns always have the exact same form in both the nominative and accusative cases. So even though the word looks unchanged, grammatically it is in the accusative case here because of the motion.
Could we just say Kötturinn hoppar á þakið without the word upp?
You could, and it would simply mean 'The cat jumps onto the roof.' Adding the adverb upp emphasizes the vertical direction, making it clear that the roof is physically above the cat's starting position.