PROJECTILE LAUNCHED AT AN ANGLE
Wait for the applet to fully load, then click "linear-linear".

Load these animations and observe ... Which ones give projectile motion?
linear-linear    linear-quadratic    quadratic-linear    quadratic-quadratic    linear-cubic

The purple ball is launched at an angle. The blue and red balls represent the x and y parametric components of the purple ball.

Look at the second animation. i.e. linear-quadratic. Consider the x-direction.  Notice that the x-coordinate of the projectile (purple) is identical to the x-coordinate of the blue ball at every instant.  What do you notice about the spacing between successive blue images?  The distances are constant, and the x-t graph is a straight line. So the motion is linear, which means that the horisontal speed is constant.

Consider the y-direction. Notice that the y-coordinate of the projectile (purple) is identical to the y-coordinate of the red ball at every instant.  What do you notice about the spacing between successive images for the red ball?  The distances get smaller as the object rises and gets larger as the object falls, so the y-motion is quadratic, as the y-t graph shows. That is because gravity excerts a force on the object, so it has a vertical acceleration of -9.8 m/s2.

Now study the other component forms. Can they give projectile motion?