syokuzi no ato, haita.

A natural reading is:

しょくじ の あと、はいた。

• 食事 = しょくじ
• の = の
• あと = あと
• 吐いた = はいた

Be careful with 吐いた: it comes from the verb 吐く (はく, to vomit / throw up), so はいた here is haita.

のあと means after ... when it follows a noun.

So:

• 食事 = meal
• 食事のあと = after the meal / after eating

This pattern is very common:

• 仕事のあと = after work
• 授業のあと = after class
• 映画のあと = after the movie

So Noun + の + あと is a basic grammar pattern for after N.

Good question. In Japanese, あと can sometimes be followed directly by the main clause, especially in simple narration.

So 食事のあと、吐いた。 is natural and understandable.

But you may also hear:

• 食事のあとで、吐いた。
• 食事のあとに、吐いた。

These are also grammatical. Very roughly:

• あと alone: plain, direct
• あとで: very common in everyday speech
• あとに: also common, sometimes a little more formal or structured

In this sentence, dropping an extra particle keeps it short and blunt, which fits the unpleasant action 吐いた.

吐いた is the past form of 吐く.

• dictionary form: 吐く
• past plain form: 吐いた

Japanese often uses the past tense simply to report a completed event, just like English threw up or vomited.

So the sentence is describing something that already happened: first the meal, then the vomiting.

The subject is omitted.

This is extremely common in Japanese when the context makes it clear or when the speaker does not want to state it directly. Depending on the situation, it could mean:

• I threw up after the meal
• He/She threw up after the meal
• They threw up after the meal

Japanese often leaves out I, he, she, etc. if they are understood from context.

Yes. 吐いた is the plain past form, so it is casual / neutral in style.

A more polite version would be:

• 食事のあと、吐きました。

This is better in polite conversation, when speaking to a teacher, customer, doctor, or someone you do not know well.

The plain form 吐いた sounds more like a diary entry, casual conversation, or simple narration.

吐く has more than one meaning.

Commonly, it means:

• to vomit / throw up

But it can also mean:

• to emit / exhale / give out
• sometimes to utter or to spit out words

For example:

• 煙を吐く = to emit smoke
• 弱音を吐く = to complain / say weak-hearted things

In your sentence, because of 食事のあと and the context, it clearly means to vomit.

Both are natural.

• 食事のあと、吐いた。
• 食事のあとで吐いた。

The version with the comma and no extra particle can sound a little more clipped, narrative, or stark. It feels like:

• After the meal, threw up.

The あとで version sounds a bit more conversational and smoothly connected.

So this is not a grammar mistake; it is just a style choice.

The comma helps separate the time phrase from the main action:

• 食事のあと、 = after the meal,
• 吐いた。 = threw up.

Japanese commas are often used more flexibly than English commas. Here, the comma gives a small pause and makes the structure easier to read.

It is especially common when a sentence starts with a time expression or setting.

Yes.

• 後 is the kanji form
• あと is the hiragana form

Both are correct:

• 食事の後、吐いた。
• 食事のあと、吐いた。

Writers often choose hiragana for readability or style, especially in simpler materials. So the choice here is not about grammar, just writing style.

They are similar, but not always identical in tone or usage.

• 食事 is a more neutral/formal word for meal or eating
• ご飯 can mean cooked rice, and also meal in casual speech

So you could say:

• ご飯のあと、吐いた。

But that may sound a little more casual, and sometimes ご飯 can be ambiguous because it also means rice.

食事 is a clear, neutral choice here.

Yes. It is short, but natural.

Japanese often allows very compact sentences when the context is known. This one has:

• a time phrase: 食事のあと
• an action: 吐いた

Because the subject and other details are omitted, it feels brief and direct. That is very normal in Japanese, especially in:

• conversation
• diary-style writing
• simple narrative
• textbook examples

So even though it may feel incomplete from an English perspective, it is perfectly normal Japanese.