curvilinear translation

Curvilinear Translation (Projectile Motion)

Projectile motion follows a parabolic trajectory. The vertical component of projectile is under constant gravitational acceleration and the horizontal component is at constant velocity. For easy handling, resolve the motion into x and y components and use the formulas in rectilinear translation.
 

At any point B

For the x-component of motion, acceleration is zero (constant velocity), thus ax = 0.

For the y-component of motion, ay = -g. Notice that the first three formulas that follow are taken from motion with constant acceleration.

At point A

At the highest point or summit, vAy = 0.

At point C

x = R, y = 0, vC = vo, and vy = -voy

Note:

vy is positive if directed upward and negative if directed downward

At any point D below the origin O, the sign of y is negative.