To get through the very first area, you will need a cutting tool to cut through the foliage (machete, hatchet, large axe, fire axe, or katana sword). Next, you have the option to rush the zed (encountering two small hordes of 2 zed each) or distract them (did not have a whistle here--does that item do anything for this encounter?). Distracting them combines the hordes into a small horde of 4.
Immediately after, a zed is killed by a survivor. You can turn around or run away--if you run, you have an option to go back to the camp and you will get another tarp. If you turn around, you can decide not to chase them; the game mentions you leaving all of the items at the campsite, but you don't actually leave them. If you decide to chase the other survivor, when you return to the camp you have the option of taking the last arrow. You can chase the survivor after turning around, and whatever cutting tool you have can be used to cut through more foliage. The Achievement section hints that there is more to the ghost encounter later to complete the ghost challenge.