Pojken kan hoppa.

Because pojken is the definite form of the noun.

• en pojke = a boy
• pojken = the boy

In Swedish, the definite article is usually added as an ending on the noun, instead of being a separate word like English the.

So:

• pojke is not a complete natural form by itself in a normal sentence
• you usually say either en pojke or pojken

Pojke is a common gender noun, so it takes en in the indefinite form:

• en pojke = a boy
• pojken = the boy

This is the normal pattern for many en-words in Swedish.

A useful mini-pattern is:

• en pojke
• pojken
• pojkar = boys
• pojkarna = the boys

Here kan means can in the sense of is able to.

It is the present tense of kunna.

• kunna = to be able to / can
• kan = can

So Pojken kan hoppa means that the boy has the ability to jump.

Hoppa is the infinitive form, meaning to jump.

After a modal verb like kan, Swedish usually uses the infinitive without att.

So:

• kan hoppa = can jump
• not kan att hoppa

This is similar to English, where we say can jump, not can to jump.

Because after modal verbs such as kan, Swedish does not use att.

Compare:

• Jag vill hoppa. = I want to jump.
  Here Swedish also often omits att after some verbs.
• Jag försöker att hoppa. / Jag försöker hoppa.
  With some verbs, att may appear or be omitted depending on the verb and style.
• Jag kan hoppa.
  After kan, you do not use att.

So kan hoppa is the correct structure.

No. In modern Swedish, verbs do not change for person.

So the verb form stays the same:

• jag kan = I can
• du kan = you can
• han kan = he can
• pojken kan = the boy can

This is much simpler than English, because Swedish does not add an -s equivalent for he/she/it.

Yes. This is the normal basic pattern for a main clause:

subject + finite verb + infinitive

So:

• Pojken = subject
• kan = finite verb
• hoppa = infinitive

This is a very common Swedish sentence structure.

Sometimes, but Swedish has important word-order rules.

In a normal statement, Pojken kan hoppa is the natural order.

If you make it a yes/no question, the finite verb comes first:

• Kan pojken hoppa? = Can the boy jump?

If you begin with another element, Swedish usually keeps the finite verb in second position:

• I dag kan pojken hoppa. = Today the boy can jump.

That verb-second pattern is very important in Swedish main clauses.

A simple learner-friendly approximation is:

• pojken ≈ POY-ken

A few notes:

• poj- sounds a bit like English boy, though not exactly the same
• the k is a normal hard k sound here
• the stress is on the first syllable: POJ-ken

The full Swedish pronunciation is more precise than the English approximation, but POY-ken is a useful start.

A simple approximation:

• kan ≈ kahn or kan with a short vowel
• hoppa ≈ HOP-pa

Notes:

• hoppa has a short vowel followed by a double consonant
• the stress is on the first syllable: HOP-pa
• the double pp affects the vowel length more than making you strongly pronounce two separate p sounds

In Swedish spelling, a double consonant usually shows that the vowel before it is short.

So in hoppa:

• o is short
• pp helps signal that shortness

This is a very common spelling pattern in Swedish.

Compare the general idea:

• short vowel + double consonant
• long vowel + single consonant

Often, but not always.

Kan can express things like:

• ability: Pojken kan hoppa. = The boy can jump.
• learned skill / knows how to: Hon kan simma. = She can swim.
• sometimes possibility, depending on context

So in this sentence, the most natural meaning is ability.

Add inte after the finite verb:

• Pojken kan inte hoppa. = The boy cannot / can’t jump.

That placement is very important in Swedish:

• Pojken
  • kan
    • inte
      • hoppa

Put the finite verb first:

• Kan pojken hoppa? = Can the boy jump?

This is the standard yes/no question pattern in Swedish.

Statement:

• Pojken kan hoppa.

Question:

• Kan pojken hoppa?

Yes, but it means something different.

• Pojken kan hoppa. = The boy can jump.
• En pojke kan hoppa. = A boy can jump.

So the difference is definite vs indefinite:

• pojken = a specific boy already known in the context
• en pojke = any boy / a boy not yet specifically identified

The dictionary forms are:

• pojke = noun base form
• kunna = infinitive of kan
• hoppa = infinitive

In the sentence:

• pojken is the definite noun form
• kan is the present tense of kunna
• hoppa is already in the infinitive form

So this one short sentence already shows several useful Swedish grammar patterns.