Video Transcript
Which of the lines shows the trajectory of a projectile?
Our diagram contains three trajectories: the purple solid line, the red dotted line, and the blue dashed line. We want to know which one shows us the trajectory, the path through space, of an object known as a projectile. In a sense, a projectile is a special kind of object. As it moves vertically and horizontally, it experiences just one force. That force acts vertically downward. This along with the initial launch conditions of the projectile determine its trajectory.
Regardless of how a projectile is launched though, if it experiences only one constant vertically downward force, then the path it follows takes on a certain shape. This shape is called a parabola. A parabola is a smooth curve that is different to, for example, a circle. That’s relevant for our question because we see that this purple solid line represents a circular trajectory. That is, this purple arc is a half circle. That path though is different from the path of a parabola.
Another thing that’s true about parabolas is that they don’t have any sharp points in them. They are smooth curves. This means that the sharp point we see in the dashed blue line indicates that this line does not show the trajectory of a projectile, that is, a parabola. That leaves us with just one trajectory, and that one does follow a parabolic path. Of these three lines, the red dotted line shows the trajectory of a projectile.
