AP Physics C/Vectors and Motion in Two Dimensions

Vectors in 2D Vectors in 2 dimensions have both an x and a y component. We can find the components if given an angle, θ, in the following manner: Projectile motion Projectile motion is one of the most common applications of 2D vectors. Lets start with an example, lets say we throw a ball 30 m/s at a 60° angle. We can figure out how far it will land and how long it will take. The acceleration in the y of a projectile motion question is always . Since velocity is the integral of acceleration, , and C will always be equal to initial velocity, . IMPORTANT: Any projectile with an initial height or y of 0 will reach the apex of its height at (where t is the total time of travel). This is because at the apex, the slope of the tangent line to the y position is equal to zero. So lets solve for time. From here we can solve for the range of the object.