The rope of climbing is described as:
This 60-foot length of silk rope weighs 3 pounds and can hold up to 3,000 pounds. If you hold one end of the rope and use an action to speak the command word, the rope animates. As a bonus action, you can command the other end to move toward a destination you choose. That end moves 10 feet on your turn when you first command it and 10 feet on each of your turns until reaching its destination, up to its maximum length away, or until you tell it to stop. You can also tell the rope to fasten itself securely to an object or to unfasten itself, to knot or unknot itself, or to coil itself for carrying.
What defines the motion of the rope? Can it ascend vertically into the air? Can it horizontally arc across a river without touching the water?
How much lifting capacity does it have? The text says the rope holds 3000 pounds. How much weight can the rope hold as it climbs into the air? For example, if the rope climbed 50 feet into the air straight, can it only support itself? Could a piece of paper or an apple be attached or would the rope collapse? Or conversely, could someone climb the rope (like Rope Trick)? Could a 3000 pound attached basket of people be moved 10 feet a round across a river?
Could the rope be used to grab someone unconscious down in a pit, lift them up to the edge of the pit, then have the rope continue to climb up to a ledge above while still attached to the person thus lifting them?