Final answer:
In projectile motion, the horizontal and vertical motions do not influence each other, meaning they are independent components. This allows for separate analyses of the two motions, exemplified by the fact that horizontally projected and free-falling objects will fall vertically at the same rate.
Step-by-step explanation:
Independence of Motion in Projectile Motion
When discussing projectile motion, the statement 'Horizontal and vertical motions of a projectile are independent of each other' means that the motion in the horizontal direction does not affect the motion in the vertical direction, and vice versa. This concept is a key part of analyzing projectile motion, as it allows us to treat the two components separately.
Therefore, the correct answer to the question is c) The two motions are unrelated. This is illustrated when comparing the trajectory of two cannonballs, one dropped in free fall and another projected horizontally; both fall at the same rate vertically, despite their horizontal motion being different.