Obedient and docile describe a person or animal who submits to the rules, requests, or power of another. One who is obedient, like a child, a servant, a worker, or a dog, does what they're told, out of a desire to please or show respect for someone of greater authority (or simply to avoid punishment). Obedient suggests a learned behavior, whereas docile suggests the nature, temperament, or state of a person or, more likely, an animal. A docile creature may be tamed or domesticated, in which case it has been, in a common phrase, rendered docile. If wild, a docile animal is non-threatening or approachable by nature (a normally docile species of shark). A docile person offers no resistance to being handled or controlled by others. Docile can suggest sweetness and gentleness, but usually it implies submissiveness and passivity: docile citizens, docile population, docile workers.
Dry and arid mean without moisture. Dry is the general word indicating absence of water (a dry well) or freedom from moisture (dry clothes). Arid has a very specific context of use. It suggests great or severe dryness in a region or climate, especially when it results in bareness or in barrenness: arid climate of Nevada; arid soil. If you wish to use it figuratively, remember it’s a harsher word than dry. We call something dry that is uninteresting or dull (a dry geography textbook). Arid suggests something devoid (barren) of interest, imagination, emotion, or vitality: an an arid performance by a burned out cast.
The verbs cross and traverse both refer to passing or extending over or across something. Saying hikers traverse or hikers cross a meadow to reach a road conveys the same information, although traverse is more formal. Note that the characteristic use of cross to mean “to intersect” or “pass over a line” cannot be replaced by traverse—that is, you can say that two paths crossed to indicate that they intersected, but not that they traversed. Traverse most often suggests passing over or covering a considerable distance, sometimes with difficulty. But it is also frequently used of physical artifacts such as pipelines, railways, roads, paths, and trails, all of which traverse regions and terrains.