A rough but serviceable bow can be made pretty quickly if you know how; maybe ten, twenty minutes wandering about in your average woodland to find a good piece (might want to cut that down if he's injured, but he may not find as good a piece) then ten minutes, twenty to remove it from the tree. The shaping can take a little while, but the stringing is pretty quick (couple of Honda knots and a quick test-draw) so you could have a bow inside a couple of hours. If you skip the shaping and just use a springy branch, then you can use a thinner piece that can be removed from the tree faster, and the shaping only takes a few minutes. It'd be less powerful though, so maybe worth doing the split-and-shape method. Arrows a little while, but for quick-and-dirty survival work you can just use sharpened straight sticks, which takes however long it takes to find something straight enough (depends on what grows bin that type of forest) plus about three minutes to whittle points onto them. They won't be brilliantly accurate without fletchings, but that takes ages, and at close range it doesn't matter too much. Without curing, the bow won't last long, but if he's a decent shot he should be able to bag something before it splits.
It's a fair bit of work for an injured man, though, and walking around finding something to shoot will be tough for him. Might be a better idea to make a sling (bootlaces and a scrap of cloth, maybe from a handkerchief) and wander about setting snares. They'd give a much better chance of catching something on way less effort, and if he sees something then he has the sling. Hit a rabbit squarely with a stone from a sling, you have a meal.
I'd suggest reading Lofty Wiseman's book on survival, and/or googling for a copy of US FM21-76, the field manual on survival, with good stuff on hunting and snares.