Learn Polish: Widziałem, jak uliczny muzyk wrzuca bilet do mojego kieliszka. - I saw a street musician drop a ticket into my wine glass.

With verbs of perception like widzieć (to see) or słyszeć (to hear), using jak instead of że emphasizes that you witnessed the action directly as it was happening. It functions similarly to an '-ing' verb in English, meaning you saw the musician 'dropping' the ticket, rather than just seeing the fact 'that' he dropped it.

Why is the verb wrzuca in the present tense if the main verb Widziałem is in the past tense?

In Polish perception clauses with jak, the subordinate clause usually uses the present tense to show that the action was happening at the exact moment you observed it. You are essentially saying, 'I saw how he is dropping the ticket.'

Could I use the perfective verb wrzucić (to complete dropping) in this structure?

Not with jak. The word jak in these perception clauses pairs with imperfective verbs to frame an action in progress. To express a completed action, you would switch back to że and use the past tense: Widziałem, że wrzucił... (I saw that he dropped...).

Why does the word kieliszek change to kieliszka?

The preposition do (into/to) always requires the genitive case. Because kieliszek is an inanimate masculine noun, its genitive form takes the -a ending here, becoming kieliszka. Notice that the 'e' also drops out, which is a common vowel shift in Polish noun declension.