Historical analysis: The lands in which they found themselves would have a great influence on Nephi's ability to make a bow. In this case, there is a general area of the Arabian peninsula where these events fit with the available landscape:
"The reason I pointed out Medina there is that along the coast here there was a German baron called Julius Euting who wrote a classic work, and he hunted everywhere. The only place in Arabia where you can find very good hunting is in the mountains along here, especially Mount Jasum and Mount Azd. Well, this is very important because they are the only places in Arabia where you can find nabc wood which is wood for bows. It makes excellent bows, but it is exceedingly rare. It's only found in the mountains right along here. This is where they would have been at that time, keeping in the mountains near the Red Sea. They came here and [their bows] lost their springs and all that. We don't know exactly where they were, but around the same area where you find the bow wood at Mount Jassum and Mount Azd, you also find very rich game--oryxes, mountain goats, everything you can imagine at the tops of the mountains (Hugh Nibley, Teachings of the Book of Mormon, Semester 1, p.218).
Nephi is not only in a place where he might hunt, he is in a place where wood for bows might be obtained. He makes a bow. Notice, however, that he also makes an arrow. David S. Fox suggests: An examination of Nephi's account shows that whoever wrote that account was familiar in some detail with the field of archery. Consider what happens to an arrow at the instant the string is released: the full force of the drawn string is applied to the end of the arrow, trying to accelerate it, but also tending to bend or buckle the arrow. If the bow's draw weight and the arrow's stiffness are not perfectly matched, the arrow will stray off the intended course or fall short of the mark. An arrow that is too flexible will leave the bow with a vibration that can cause the arrow to behave erratically. On the other hand, an arrow that is too stiff is probably too heavy for the bow.
Nephi's steel bow likely used heavier, stiffer arrows than his simply fashioned wooden bow could handle. Nephi was physically large (see ! Nephi 2:16; 4:31), and he would have had little reason to use a bow made from metal if he did not have considerable strength. The arrows to match the steel bow used by such a man would undoubtedly have been quite heavy in order for them to be of adequate stiffness. One experienced archer reports, "The arrows from the steel bow when shot from the wooden bow would be like shooting telephone poles." Hence, it is accurate that Nephi should mention, in one and the same breath, the fact that he made an arrow as well as a bow. Bow wood and arrow wood from the same tree or area could be matched as well." ("Nephi's Bows and Arrows", in Reexploring the Book of Mormon. FARMS 1992, pp. 41-42).
It is interesting, in addition, that while Nephi made a new bow and arrows, he was also armed with a sling and stones. He is preparing for this important task as well as possible, and taking all possible weapons for obtaining food. He knows he cannot fail.
Scriptural analysis: After Nephi makes his bow and arrow, he goes to his father to ask where to go. On the one hand, this may be seen as respect for elders, or respect for the designated priesthood leader. On the other, given Lehi's murmurings, it is also a very gentle and kind call to repentance - through appropriate action. Nephi restores his father's place at the head of the family, restores Lehi's place as the prophet of their family's exodus, and restores his father's confidence - all by the simple act of asking for guidance.
The murmurings of Lehi I have suggested indicate that the Lord held back the solution to the problem in favor of Nephi finding the solution, which he did. Nephi is being prepared to be the prophet and leader in the New World, and this experience places him in a critical position, where the welfare of his own is at risk, and he must find a solution. Nephi understands that the solution lies in two locations, the strength of his hands (by which he forms a bow and arrow) and the strength of his spirit (through which he seeks the counsel of the Lord for the location of the hunt).