"Well Zimmer, first we'll cut ourselves a short length of rope and see how much it weighs, and how much weight it can hold, assuming it meets the standards we'll prepare 4 lengths of rope about half again as long as the gorge, and we'll attach one to a heavy grapple if we can rig one up or a big log with some spikes in it, we'll attach the other end to something hefty on our side, and fire it. First of course we'll lob a few object of similar weight and size over to get an idea were it would land so we can aim... it wouldn't do to overshoot, sturdy rope or not it would probably snap if it ran out of rope while still in the air, and we do want to try to land our makeshift grapple somewhere where there is rough ground or debris to snag on."

Reality Check Metagame: Since rope varies a lot on construction I'll just utilize the default D&D 3.5 hemp rope, which is safely inside the realm of non-fantastic, they actually did their research a bit.

3.5 PHB list hemp rope being 10 pounds per 50 feet or approx. 4 kg per 15 meters. To keep numbers even we'll use 120 meters, or 4x8=32 kg. It also lists the break DC as 23, which if we assumed indicated it could hold a weight equal to the max carry of a strength 23 character, which would imply a character of a non natural 20 roll to break it would require a +4 modifier, or a strength of 18, so it seems the max lift of a strength 18 character should be well within the safe tolerance of such a rope, for strength 18 character the max carry is 300, or 600 lift over their head, which seems a better choice since the effort to break a rope is more akin to a short heavy exertion then walking all day carrying something. So the rope should be able to hold 600 pounds quite safely (which is safely inside the realms of reality) so that the rope can hold 270 kg, minus its own weight, 238 kg, minus the weight of a second rope, 206 kg, minus say 106 kg for a decently muscled and athletic person and some a backpack with a canteen, a meal, some simple light tools, etc, which is probably on the heavy side, still leaving us another 100 kg of extra tolerance.

"After we have our grapple hooked, we'll have a few stout men pull on it to make sure it doesn't tug free, then we'll send a man across with another piece of rope tied to him he can secure on the other end or we can use to drag him out of the water. We'll make sure he's got some simple tools and supplies too, and rig him up a harness so he can rest along the way, a few leather belts should do for that. Then we'll send a couple more ropes across the same way. Now we just need a volunteer, someone who is in good shape I should think..." Says Titus, looking over at the legionnaires and raising an eyebrow. "Once we've four ropes up we can commence sending across some harnesses on pulleys full of timber and tools, and re-tie everything into the right shape for a rope bridge, and start building that."