Les cerceaux que j'ai vu lancer sont tombés dans l'eau.

Questions & Answers about Les cerceaux que j'ai vu lancer sont tombés dans l'eau.

Why is it j'ai vu and not j'ai vus, since les cerceaux comes before the verb?
This is the exact exception for verbs of perception (like voir or entendre) followed by an infinitive. Normally, the past participle agrees with a preceding direct object. But here, the hoops (les cerceaux) aren't doing the throwing (lancer); they are being thrown. Because they are the object of the infinitive rather than its subject, vu does not agree and remains invariable.
When would vu actually agree before an infinitive?
It agrees only if the preceding direct object is the one doing the action of the infinitive. For example, if you saw dogs running: Les chiens que j'ai vus courir. Because the dogs are the ones doing the running, vus gets an s to agree with them.
Why does tombés get an s later in the sentence?
The second part of the sentence uses sont tombés. The verb tomber requires être in the past tense, and past participles used with être always agree with their subject. Since the subject is Les cerceaux (masculine plural), tombés takes an s.
Why is lancer in the active infinitive form instead of a past participle like lancés to mean thrown?
In French, verbs of perception use an active infinitive for actions happening in the moment you observe them, even if the English translation feels passive like thrown or being thrown. French avoids using a passive structure here, so you simply use the infinitive lancer.

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