Projectile trajectories - With and Without Air Friction

All of us are familiar with the arch-shaped path, or trajectory, a ball follows when we throw it. When symmetric, this is a parabola, and is the common shape we use in physics classes for projectiles. But WHY is it an arch of any kind, let alone a parabola? And why are we lying to you about projectiles???

We ignore air friction when we do projectile problems, but in life this makes it more complicated, and also no longer a perfect parabola. Check out this video to get a sense of why parabolas form when there is no air friction, and what the trajectory looks like in a more realistic environment, with air friction.