How does projectile motion relate to linear motion?
Projectile motion relates to linear motion in a sense that it is a projection of components of linear motion in 3-dimensions.
Say one throws a ball in the air and it follows a projectile path. It is going both forward and up at the same time- therefore having two types of linear motion. One is in the x-direction, and the other is in the y-direction.
Interestingly, these two component's of the ball's motion are independent of each other and can be split up. The other thing they share in common is the amount of time it takes them to finish their trajectory (finding the common time is often the key to solving projectile motion problems). Otherwise, the x-movement and the y-movement can be split up and their respective equations can be used to make the problem easier.
It is important to note that the horizontal component of the velocity doesn't change throughout the trajectory- But the vertical component continuously does (since it is pulled down by gravity).