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I can't find anything about this in the PHB, but it seems to me that it would make sense to include some kind of penalty when making a ranged attack against a moving target, especially if it is moving fast.

For the archer, a massive orc standing in front of the tank is surely easier to hit than an eagle plunging down on some other party member at full speed. Sure, the archer can try to predict the target's trajectory, and might be able to hit nevertheless, but it will definitely be harder.

Yet, as long as the target is within range (as far as I can see from the rules), a normal attack roll is made against the opponent's AC in both cases. The AC may model the armor's quality, the dexterity of a target, perhaps even some shielding buff, but it does not include the speed a target is moving at.

Wouldn't it make sense, for instance, to impose disadvantage on the attack roll in a situation where the target of a ranged attack is moving rapidly, such as in the case of the plunging eagle?

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No, not by default. But see below!

The simulation provided by D&D 5e (and previous editions) isn't that detailed. Fast-moving targets are the same as slow-moving targets. (Immobilised targets are easier to hit, but that's a different situation entirely.)

However, D&D 5e in particular is designed so that intuitions like yours are trivially integrable into situations where the DM thinks they should matter. This makes the answer vary from table to table, hence the "no, by default" default answer.

Instead of a list of situational modifiers, 5e bundles every tactical advantage and disadvantage into one mechanic, Advantage and Disadvantage: a character that has advantage rolls twice and takes the better result; one with disadvantage rolls twice and keeps the worse result.

If the DM deems a particular target's speed to create a disadvantage for ranged attackers, then the DM can impose disadvantage on their attack rolls.

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