Write the equations of motion for constant acceleration and describe each term involved. Explain how to apply these equations of motion to calculate the horizontal and vertical components of a projectile moving under the force of gravity only.

The equations of motion for constant acceleration are obtained from Newton's laws of motion. They are sometimes known as the SUVAT equations and can be used to calculate components of a projectile's motion by applying the equations, separately, to each component of the projectile's motion.
The trick is to list the variables which you know and the one(s) you want to find out then apply your SUVAT equations separately to each component (direction) of the projectile's motion.