Parametric Curves, Part 25 (Modeling the Motion of a Ball (a 'Projectile'), Part 4

Modeling the trajectory of a ball (a "projectile"), Part 4. With straight-line motion, we first calculated dist(t) = (distance traveled from time zero to time t) using the Pythagorean Theorem (the distance formula), then we differentiated this function to get speed(t) = (instantaneous speed at time t). With curved motion, we first calculate speed(t) as the length of the velocity vector v(t) (which is the derivative of the position vector) and then we integrate to get dist(t). That is, the area under the speed graph from time 0 to time t is the value dist(t).