The projectile is a classic mechanics style question. Lots of resolving vectors and using SUVAT formulae – what more could a physicist want?
There are variations on a theme but you can see a break down of the problem here: http://www.physicsclassroom.com/class/vectors/u3l2a.cfm.
Phet is a load of physics animations paid for by some Nobel prize money. Here is one on projectiles to play with: http://phet.colorado.edu/sims/projectile-motion/projectile-motion_en.html.
Here are some videos of this kind of thing:
The monkey and the hunter is a classic example of projectile motion. The question goes that you want to shoot a monkey. The is a clever monkey and as soon as you fire it will drop out of it’s tree. Where should you fire to hit the monkey. I once attended a lecture where they had build an air rifle with laser sight and video mounted on it to show how the theory works in practice.
This is an explanation of how it works: http://www.nationalstemcentre.org.uk/elibrary/resource/2084/monkey-and-hunter.