Cavalier Order of the Seal Challenge ability

[Durinor]

The Cavalier’s challenge ability reads as follows:

Challenge (Ex)
Once per day, a cavalier can challenge a foe to combat. As a swift action, the cavalier chooses one target within sight to challenge. The cavalier’s melee attacks deal extra damage whenever the attacks are made against the target of his challenge. This extra damage is equal to the cavalier’s level. The cavalier can use this ability once per day at 1st level, plus one additional time per day for every three levels beyond 1st, to a maximum of seven times per day at 19th level.
Challenging a foe requires much of the cavalier’s concentration. The cavalier takes a –2 penalty to his Armor Class, except against attacks made by the target of his challenge.
The challenge remains in effect until the target is dead or unconscious or until the combat ends. Each cavalier’s challenge also includes another effect which is listed in the section describing the cavalier’s order.

The Order of the Seal order effect reads:

Challenge: An order of the seal cavalier can make a free bull rush or trip combat maneuver anytime he takes the full-attack action against the target of his challenge. This free combat maneuver does not provoke an attack of opportunity.

My question is, can the cavalier use this free bull rush or trip with a ranged weapon?

[Claxon]

Well, only a cavalier's melee attacks deal extra damage, so wouldn't get the damage bonus with ranged weapons. While a strict reading of RAW would imply that the Order of the Seal grants the ability to make a free bull rush or trip with any weapon used to make a full attack action, based on specific archetypes which exist specifically to allow characters to use ranged weapon to perform combat maneuvers the logical answer is no, you cannot.

Please note that trip says "in place of a melee attack" as does bull rush. So no, they cannot be made as ranged attacks without taking the Archer (fighter archetype) or a class granting similar abilities.