Badmintonovou raketou zasáhnu badmintonový míček.

Because they are in different cases, and they also modify nouns of different grammatical genders/forms.

• badmintonová raketa = badminton racket
• badmintonový míček = badminton shuttlecock / ball

In the sentence:

• badmintonovou raketou is in the instrumental case: it expresses the tool/instrument used to do the action.
• badmintonový míček is in the accusative case: it is the direct object, the thing being hit.

So the adjective changes its ending to match the noun’s:

• gender
• number
• case

Here:

• raketa is feminine singular, so in the instrumental it becomes raketou, and the adjective becomes badmintonovou
• míček is masculine singular, and its accusative here looks like the nominative, so it stays míček, with badmintonový

It is the instrumental singular.

Czech often uses the instrumental case to show what you use to perform an action.

So:

• Badmintonovou raketou = with a badminton racket / using a badminton racket

There is no preposition here, because Czech can express this idea with the instrumental case alone.

Compare:

• Píšu perem. = I write with a pen.
• Krájím nožem. = I cut with a knife.
• Badmintonovou raketou zasáhnu... = I hit ... with a badminton racket.

This is a very common Czech pattern.

Because Czech does not need a separate word like with in this kind of sentence. The meaning with/by means of is built into the instrumental case.

So English says:

• with a badminton racket

But Czech simply says:

• badmintonovou raketou

The ending -ou on raketou and -ovou on badmintonovou already signal that role.

Be careful: Czech s can also mean with in the sense of together with someone/something, but that is a different use.

• Jdu s kamarádem. = I’m going with a friend.

That is different from the instrumental of means/tool:

• Píšu perem. = I write with a pen.

It is a direct object, so it is indeed in the accusative case. But for many masculine inanimate singular nouns, the accusative has the same form as the nominative.

So:

• nominative: badmintonový míček
• accusative: badmintonový míček

That is why it looks unchanged.

The adjective also stays the same here:

• nominative masculine inanimate singular: badmintonový
• accusative masculine inanimate singular: badmintonový

So even though it is grammatically accusative, it looks just like the basic dictionary form.

It is masculine inanimate.

That matters because masculine animate and masculine inanimate nouns behave differently, especially in the accusative.

For example:

• vidím psa = I see a dog
  (pes is masculine animate, so the accusative changes)

• vidím stůl = I see a table
  (stůl is masculine inanimate, so the accusative often looks like the nominative)

Here, míček is treated as an object, so it is masculine inanimate.

That is why:

• badmintonový míček remains badmintonový míček in the accusative

Zasáhnu is the 1st person singular form of the verb zasáhnout.

In this sentence it means something like:

• I will hit
• I will strike
• I will make contact with

Depending on context, zasáhnout can also mean:

• to hit a target
• to strike something
• to affect something
• to intervene

In your sentence, it means physically hitting the shuttlecock/ball with the racket.

So:

• zasáhnu míček = I will hit the shuttlecock/ball

Because zasáhnout is a perfective verb.

In Czech, perfective verbs usually do not express a present ongoing action. Their present-tense forms normally refer to the future.

So:

• zasáhnu literally looks like a present form
• but its meaning is usually future: I will hit

This is a very important Czech pattern.

Compare:

• zasahovat = imperfective = to be hitting / to hit repeatedly / to be affecting
• zasáhnout = perfective = to hit successfully / to strike once / to reach the target

So:

• Zasahuji míček. would sound unusual here and would not mean the same thing
• Zasáhnu míček. = I will hit the shuttlecock

The dictionary forms are:

• badmintonový = badminton
• raketa = racket
• zasáhnout = to hit / strike / affect
• badmintonový = badminton
• míček = little ball; in sports context, shuttlecock/ball depending on what is meant

So the sentence contains these base words:

• badmintonová raketa
• zasáhnout
• badmintonový míček

The actual sentence changes the forms because of case and conjugation:

• badmintonová raketa → badmintonovou raketou
• zasáhnout → zasáhnu
• badmintonový míček stays badmintonový míček

Yes. Czech word order is much more flexible than English word order because case endings show the grammatical roles.

The original sentence is:

• Badmintonovou raketou zasáhnu badmintonový míček.

But you could also say:

• Badmintonový míček zasáhnu badmintonovou raketou.
• Zasáhnu badmintonový míček badmintonovou raketou.
• Badmintonový míček badmintonovou raketou zasáhnu.

These versions can sound different in focus or emphasis, but the core meaning stays similar because the endings show what is the instrument and what is the object.

The original order feels fairly natural if you want to foreground the means or create a neutral descriptive sentence.

It can be understood, but in real Czech the more usual sports term is often:

• košíček = shuttlecock

So many speakers would naturally say something like:

• Badmintonovou raketou zasáhnu košíček.

That said, míček literally means small ball, and learners may encounter it in broad or simplified contexts. It is understandable, but for actual badminton vocabulary, košíček is often more idiomatic.

Because that is the normal position for most descriptive adjectives in Czech.

So:

• badmintonová raketa
• badmintonový míček

This works much like English:

• badminton racket
• badminton shuttlecock/ball

Czech can sometimes place adjectives after nouns, but that is not the regular pattern for ordinary descriptive adjectives like this.

You can see it from agreement.

In Czech, adjectives agree with their nouns in:

• gender
• number
• case

So:

• badmintonovou matches raketou

  • feminine singular instrumental

• badmintonový matches míček

  • masculine singular accusative/nominative-looking form

That tells you which adjective belongs to which noun.

This agreement system is extremely helpful in longer Czech sentences.

A more basic breakdown would be:

• Badmintonová raketa zasáhne badmintonový míček.
  Grammatically possible, but now the racket becomes the subject, which changes the structure.

If you want to keep the meaning I hit the shuttlecock with a badminton racket, the dictionary-style underlying pieces are more like:

• zasáhnout míček raketou
• badmintonová raketa
• badmintonový míček

Then you apply the correct forms:

• raketa → raketou
• badmintonová → badmintonovou
• zasáhnout → zasáhnu

Result:

• Badmintonovou raketou zasáhnu badmintonový míček.

Yes, depending on nuance.

Some related verbs are:

• zasáhnout = to hit, strike, reach the target
• udeřit = to strike, hit with force
• trefit = to hit a target, to hit correctly

For sports contexts, trefit or zasáhnout can both make sense depending on what you want to emphasize.

• Zasáhnu míček. = I will strike/contact the ball/shuttlecock.
• Trefím míček. = I will hit the ball/shuttlecock successfully.

Zasáhnout can sound a bit more like make contact with / strike, while trefit often emphasizes hitting the target accurately.

Roughly:

• za-sáh-nu

A few points:

• á is a long vowel, so hold it longer than short a
• h is pronounced clearly
• nu is a normal noo-like ending

So the stress is still on the first syllable of the word, because Czech stress is almost always on the first syllable:

• ZA-sáh-nu

Even though á is long, the stress does not move there.

Yes, it is grammatically correct and understandable, but in real life a speaker might choose slightly different wording depending on context.

Possible more natural versions:

• Badmintonovou raketou zasáhnu košíček.
• Zasáhnu košíček badmintonovou raketou.

Why?

• košíček is often more idiomatic than míček for badminton
• speakers may choose a word order based on emphasis

So the sentence is useful for learning:

• instrumental case
• adjective agreement
• perfective future meaning

Even if a native speaker might tweak the vocabulary a little in a sports context.