What does a derivative do?
Taking the derivative of a function is a way of determining the function's rate of change at any given point. In many applications of science and engineering, finding the derivative of the function is necessary to find other useful quantities which represent the way a system behaves.
How do you find a certain form of an equation?
In order to find the desired form of an equation, algebraic rules must be applied which transform the equation into the desired form. Any operation which does not change the fact that both sides of the equation are equal can be performed. By performing various operations which allow for terms to be canceled and moved around, the desired form can be achieved.
How does gravity affect projectile motion?
Most projectile motion problems are described in a way which neglects air and wind resistance. Because of this, gravity is the only force which acts on the projectile's vertical motion component or the y-direction (given standard cartesian coordinates). This means that the horizontal motion component or x-component of the projectile will remain constant while the vertical motion component changes at a rate of (g) or the acceleration due to gravity.