This applet invites you to explore a lot of different aspects of projectile motion: equations of motion, thrown vs dropped objects, air drag, numerical approximation.

Animate the initial angle slider. (right-click or ctrl-click or 2-finger-click) What do you observe about the behavior of:
horizontal distance traveled?
time in the air?
maximum height?
Now, show how these results can be obtained analytically (you may wish to assume starting at (0,0) for simplicity).
Comparing thrown and dropped objects
What physically does it mean when the projectile and dropped paths cross below the horizontal axis?
What variable is most important to insuring the paths cross above the horizontal axis?
What launch angle causes the the paths to cross at the same time (the objects to collide)?
Find a set of pairs of distances that for each time interval match for the two objects.
How/where do these identical pieces show up in the equations you wrote for the motion of the two objects?
Show the discrete approximations
Generally, how does the motion with air resistance compare to motion without air resistance?
What launch angle gives maximum horizontal distance? Is this the same angle as without air resistance? How does the angle depend on the drag coefficient?
Where do the paths of the dropped and thrown objects intersect with air resistance? Are the objects at that point at the same time?