Differences in prallen, aufprallen, aufspringen, zusammenstoßen

Question

I was wondering if you could help me understand the overlaps between some of these words. Dictionaries have me going in circles. The first difficulty is

1. Er ließ den Ball aufspringen.
2. Er ließ den Ball aufprallen.

Are both of these, "he bounced the ball", and 100% synonymous?

My second difficulty:

3. Die Autos prallten aufeinander.
4. Die Autos prallten aneinander.

And also

5. Das Auto prallte auf die Wand auf.
6. Das Auto prallte gegen die Wand.

Lastly:

7. Unsere Füße stießen unter dem Tisch miteinander zusammen.
8. Unsere Füße prallte gegeneinander unter dem Tisch.

I know this is a long question, but everything seems to be translated as the same thing, and I suspect that there has to be important differences.

Answer 1

I am a native german speaker from Berlin, Germany and in my Opinion the differences of your examples are as follows:

1. Er ließ den Ball aufspringen.
   
2. Er ließ den Ball aufprallen.

"Aufspringen" more means the fact that the ball really has to jump up in the air again. "Aufprallen" literally means that the ball hits the ground.

3. Die Autos prallten aufeinander.
   
4. Die Autos prallten aneinander.

In my opinion "prallten aufeinander" describes that two cars had a frontal crash, while "prallten aneinander" means that both cars had a sideways crash.

5. Das Auto prallte auf die Wand auf.
   
6. Das Auto prallte gegen die Wand.

Both sentences actually mean the same but the first sentence is really uncommon.

7. Unsere Füße stießen unter dem Tisch miteinander zusammen.
8. Unsere Füße prallte gegeneinander unter dem Tisch.

Also here both sentences actually mean the same but "stießen miteinander zusammen" is actually softer than "prallten gegeneinander". "prallten" is a little bit more a rough hit.

I hope this may helped you out.

Answer 2

Mark extended his question in one of the comments:

I will make a guess. Prallen = hit. Zusammenstoßen mit = run into/bump into, also etwas schwächer als "hit". Aber besteht ein großer Unterschied zwischen "aufprallen" und "prallen"? Ich werde einfach aus den von den Wörterbücher angebebenen Vorschläge nicht schlau.

Let's have a look at real-world use-cases of the two verbs.

Good, well-formed sentences are:

Das Auto prallte gegen die Betonwand.

Das Auto prallt mit dem Lastwagen zusammen

Der Ball prallt gegen die Decke.

However:

*Der Ball prallt.

This is not a well-formed sentence.

We learn: prallen cannot be used as such. It always (!) is accompanied by some prepositions of place.

Modifications of prallen such as aufprallen and abprallen

These are well-formed sentences:

Der Ball prallt von der Decke ab.

Die Mondfähre prallt auf den Kratergrund.

Die Mondfähre prallt auf dem Kratergrund auf.

_{In order to avoid misunderstandings: we are speaking here of a catastrophic full-speed landing, not a regular smooth landing, which, as a commenter correctly stated, would best be phrased like: Die Mondfähre setzte auf dem Kratergrund auf.}

Notably we here have aufprallen auf which should be tautological, but still it is an acceptable, well-formed use of the verb. But note the use of accusative vs. dative in the two senteces: prallen auf + accusative; aufprallen auf + dative. (You could start a discussion here if also Die Mondfähre prallt auf den (Akk!) Kratergrund auf is a well-formed sentence. I would rather say not, but I am not sure what others would say.)

These sentences are well-formed, but unusual:

Der Ball prallt ab.

Die Mondfähre prallt auf.

They are unusual because in real-life situations you practically always would add information about place (von was, auf was). With the above wording, I can them imagine occur only in textbooks and grammar treatises (like this one).

Can we derive a rule from these examples? - Here is my attempt of a rule (ad hoc): 1) "Prallen cannot stand alone. 2) Aufprallen and abprallen can principally stand alone. 3) There is no essential difference in meaning between prallen and aufprallen other that in aufprallen the information on the place is partly included.

I am afraid this answer will not really help you. Memorizing such complex rules is more brain-consuming than memorizing (= getting used to) usage it self in the form of model sentences that are acceptable.