For Projectile Motion, consider an object that is launched with an initial velocity of at an angle of . We can think of this as a vector and break it into the horizontal and vertical components.
The horizontal velocity will start as . Gravity does not affect the horizontal velocity, which means that the horizontal displacement will be:
The vertical velocity will start as , but gravity does affect this. From Physics, you can recall that the vertical displacement can be found using , where is acceleration, which we can call for acceleration due to gravity. Also, our object may not start at the ground level, so we can adjust the vertical displacement by adding the initial height, :
So we have a pair of parametric equations:
If we are using metric units, , in standard units,
Try changing the initial velocity and angle to see how the graph will change. You can zoom and move the graph as needed to see the details.