Po wywrotce używamy rzutki ratowniczej.

Because po here means after, and in this time expression it requires the locative case.

The basic form is wywrotka.
Its locative singular form is wywrotce.

So:

• wywrotka = base form
• po wywrotce = after a/the capsize

This is similar to other common phrases such as:

• po pracy = after work
• po obiedzie = after lunch

In this sentence, wywrotka means a capsize or overturning, especially in a boating, kayaking, or rescue context.

Like many Polish words, it can have different meanings in different situations. Outside this context, wywrotka can also mean other kinds of overturning. Here, though, the meaning is clearly related to water rescue or paddling.

Używamy is the present tense of the imperfective verb używać.

Here Polish uses the present tense to describe a general rule, procedure, or instruction:

• Po wywrotce używamy rzutki ratowniczej = After a capsize, we use a rescue throw bag.

It sounds like a general statement about what one does in that situation.

By contrast:

• użyjemy would mean we will use
• it would sound more like one specific future action

So używamy is natural if the sentence is giving instructions or explaining normal practice.

Not necessarily in the literal English sense.

Polish often uses first person plural to give instructions in a general, inclusive way, similar to English:

• We do this next
• After that, we use...

So używamy can mean:

• we use
• one uses
• you use, in an instructional sense

It is a common way to explain procedures.

Also, Polish does not need the pronoun my for we, because the ending -my already shows the subject.

Because the verb używać normally takes the genitive case in standard Polish.

The dictionary form is:

• rzutka ratownicza

But after używamy, it changes to the genitive:

• rzutki ratowniczej

So:

• rzutka → rzutki
• ratownicza → ratowniczej

That is why the full phrase becomes używamy rzutki ratowniczej.

It is a piece of rescue equipment used especially in water sports and rescue situations.

In English, depending on context, it is often translated as:

• rescue throw bag
• throw line
• rescue throw rope

It is something you throw to a person in the water so they can be pulled to safety.

In Polish, adjective position is more flexible than in English.

A basic descriptive adjective often comes before the noun, but in many established terms, classifications, and technical names, the adjective often comes after the noun.

So rzutka ratownicza sounds like the normal name of a specific type of equipment: a rescue throw bag.

If you moved the adjective, it might sound less like the standard term.

It can mean either one, depending on context.

Polish has no articles, so it does not directly mark the difference between:

• a capsize
• the capsize

You understand that from the situation.

So:

• in a general instruction, it may mean after a capsize
• in a specific story or discussion, it may mean after the capsize

A rough pronunciation guide is:

po wywrotce używamy rzutki ratowniczej
po vuh-VROT-tseh oo-zhih-VA-mih ZHOOT-kee ra-tov-NYAY-shay

A few useful sound notes:

• w sounds like English v
• rz usually sounds like the s in measure
• cz sounds like ch in chop
• u sounds like oo
• y has no exact English equivalent; it is a harder vowel than i

The trickiest words are often:

• wywrotce
• używamy
• rzutki
• ratowniczej

Yes. A few possible alternatives are:

• Po wywrotce używa się rzutki ratowniczej.
  This is more impersonal: After a capsize, a rescue throw bag is used.

• Po wywrotce należy użyć rzutki ratowniczej.
  This means: After a capsize, one should use a rescue throw bag.

• Po wywrotce posługujemy się rzutką ratowniczą.
  This uses a different verb, posługiwać się, which takes a different case.

Your original sentence is natural and clear, especially in instructional language.