The two-dimensional motion of an object launched with both a horizontal and a vertical component of velocity and falling under the influence of gravity alone is called projectile motion.

			Horizontal motion is not affected by gravity.

			Vertical motion is affected by gravity.

			Motion in the horizontal direction is independent of motion in the vertical direction.

			The trajectory (path in two-dimensional space) of a projectile is a parabola.

			If air-resistance can be neglected, then a projectile takes the same time to reach its peak as it does to return to the height at which it was launched.

			The maximum height of a projectile is the same as the maximum height of an object thrown straight up with the vertical component of the launch velocity.  Vertical velocity as a function of time:  vy = vo sin(θ)*t - (1/2)gt2.  Set vy = 0 to find time to reach peak.  Find the area under the vy-t graph to find the peak height.

			Since the horizontal velocity is constant at vx = vo cos(θ), if we know how long the projectile is in the air, we can multiply that time by vx to get the horizontal distance traveled.  The time the projectile is in the air is twice the time it takes to reach its peak height, which we find by setting vy = vo sin(θ)*t - (1/2)gt2 = 0 and solving for t.  So, the horizontal range of a projectile is R = 2*t*vo cos(θ).