### Video Transcript

Which of the following is a correct statement about the trajectories shown? (A) Only the trajectories that have the same maximum horizontal displacement are examples of paths of objects in projectile motion. (B) Only the trajectories that have the same maximum vertical displacement are examples of paths of objects in projectile motion. (C) All of the trajectories shown are examples of paths of objects in projectile motion. And (D) none of the trajectories shown are examples of paths of objects in projectile motion.

The trajectories we’re considering are these four shown here. All four of our answer options make claims about projectile motion. An object can be considered a projectile when it’s moving through the air subject to only one constant downward-acting force, the force of gravity. A projectile then experiences no force in the horizontal direction. This is why all four of these trajectories are symmetric about a vertical line through their center. They don’t accelerate in that direction because there’s no horizontal force.

If we think about objects moving through the air subject only to the force of gravity, we know that those moving objects can potentially follow many different paths. For example, if we imagine a small object, like a stone, at the beginning of the purple and green paths, we may be able to throw the stone, say, so that it follows either one of these paths. The same thing is true for the red and blue trajectories. There’s no minimum or maximum horizontal or vertical displacement required for an object’s path to be projectile motion.

Considering again or answer options, we can therefore eliminate options (A) and (B) from consideration. Option (D) that remains says that none of these trajectories represent projectile motion. But we’ve seen that, rather, all these paths are possible paths for an object, like a stone, to fly through the air. Therefore, all of the trajectories are examples of paths of objects in projectile motion. This corresponds with answer option (C). All of the trajectories shown are examples of paths of objects in projectile motion.