Which of the lines shows the trajectory of a projectile?
We see here three lines: a purple dotted line, a green solid line, and a yellow dashed one. To find out which one shows us the trajectory of a projectile, we want to recall that all projectiles follow a certain kind of path. Say that we pick up a stone off the ground and then rear back and throw the stone through the air. By doing this, we’ve created a projectile. A projectile is any object that moves under the influence of no forces except one.
A constant vertically downward force acts on every projectile. This force, along with the way that a projectile is launched, determines its trajectory. But interestingly, no matter how a projectile is launched, whether we throw it high or low or somewhere in between, all of these possible paths are described by a mathematical shape called a parabola. A parabola is a smooth curve, and that by itself tells us something about our answer.
Notice that the yellow dashed line is not smooth but has this bend in. This trajectory then does not follow a parabolic path, and therefore it can’t represent a projectile’s motion. If we look closely at the dotted purple line, we see that for a significant part of this trajectory, the curve is flat. This doesn’t agree, though, with an object that experiences a constant, vertically downward force. When such a force acts on an object, that object’s path will not have a flat horizontal portion. This means we can cross out the dotted purple line too. That also doesn’t show us the trajectory of a projectile.
The only remaining line, the solid green one, does. This is a possible path through space for an object experiencing only a vertically downward force. The solid green line then shows the trajectory of a projectile.