Projectile Motion

[MechEng83]

In the numerous threads, I've seen statements that shows me a lot of posters only know enough about projectile motion to be dangerous. I hope to clarify a few points, which should be applicable regardless of how you launch the game piece. Caveat: this discussion will neglect air resistance.

False: The ball will travel in a straight line before it falls.
Truth: The path of a projectile is a parabola.
Clarification: If your speed is fast enough, you can approximate the path as a straight line until the gravitational acceleration becomes significant.

False: 45 degrees is the "best" launch angle to get over the truss/in the high goal.
Truth: Maximum horizontal distance when the ball returns to its starting height is achieved when the projectile is launched at 45 degrees.
Clarification: Assuming a fixed launch speed, a steeper launch angle will cause the ball to travel higher, which means it's in the air for a longer period of time. When launching from a height above zero, an angle less than 45 degrees gives the furthest horizontal distance. (For those of you more advanced in mathematics, solve for the slope of the parabola at the point it hits the ground to be -1)