Well a roller coaster works because of two principles, Kinematics and Dynamics. First of all we have to understand Newtons three laws:
Newton's first law- law of inertia : All objects will remain in a state of rest or continue to move with a constant velocity unless acted upon by an unbalanced force.
Newton's second law : The acceleration of an object depends inversely on its mass and directly on the unbalanced force applied to it.
Newton's third law : For every action force, there is an equal and opposite reaction force.
Those laws would prove that Roller coasters have force applied on them in order for them to move. With a force of gravity acting against and along with it, the roller coaster is able to gain speed to fulfill the entrainment which people require for amusement. So we see Newton's first law applied as the roller coaster does not move unless there is a chain dragging it against gravity, and gravity acting on it as it goes down. Then we see Newton's second law as the weight of the people on the coaster and the coaster itself will affect the free fall or the fall of a roller coaster. Lastly, we see Newton's third law as for the against gravity movement, there is a along gravity movement.
Vector Addition
Vector addition is the addition of vectors. You basically need to understand that you are adding the directions along with the length. So first, before we move on to an example, you need to recall the Pythagorean Theorem which is A^2 + B^2 = C^2
The vector addition is similar to that, because it is just one unknown side (usually the hypotenuse) then two known sides, which then will lead to the square of the two known numbers followed by the addition of both known numbers.
