Which of the lines shows the trajectory of a projectile?
In our diagram, we see three different trajectories: one indicated by the dashed green line, one by the solid purple line, and one by the dotted red line. We want to choose which one shows us the trajectory of a projectile.
A projectile is a type of object that moves only under the influence of a constant, vertically downward force. Typically, this is the force of gravity, say, acting on a ball that we throw into the air. When an object is launched from the ground so that its speed has both a vertical as well as a horizontal component, that projectile follows a path known as a parabola. This is a mathematical shape that describes the trajectory of all projectiles.
A parabola could look like this or like this or like this, and there are many other such possibilities. For our purposes, one important thing to realize about parabolas is that they are different from circles. A parabolic path is different from a circular one. And in our diagram, we see that the solid purple line is indeed a circular path. This means we won’t choose this path as one representing the trajectory of a projectile.
Notice that all three of these trajectories have the same maximum displacement. For a parabolic path that has the same maximum displacement as a circular one, the parabolic path will fit entirely inside that circular path. In other words, it will always be inside or overlap with that circular arc.
Considering our answer options, we see that the red dotted line goes outside our purple circular arc. This trajectory, therefore, can’t represent the trajectory of a projectile. The green dashed line, however, does have a parabolic shape. This is the one that shows the trajectory of a projectile.