Final answer:
The horizontal velocity of an object projected horizontally off a cliff remains constant as there is no horizontal acceleration in such two-dimensional projectile motion, which ends with a parabolic trajectory upon impact.
Step-by-step explanation:
When an object is projected horizontally off a cliff, its horizontal velocity remains constant due to the absence of horizontal forces acting on it (assuming air resistance is negligible). This concept is a part of analyzing two-dimensional projectile motion, where the motion is broken into two components: horizontal and vertical.
The horizontal component (ᵛₓ) is unaffected by gravity because there is no horizontal acceleration (ax = 0), thus the velocity in the horizontal direction is uninterrupted. In contrast, the vertical component is influenced by gravity, which causes the object to accelerate downward (the acceleration due to gravity is typically approximated as 9.81 m/s² on Earth). Bringing both motions together, the object follows a parabolic trajectory culminating in its impact with the ground. It's important to understand that the horizontal motion does not affect the rate at which the object falls; it falls at the same rate as any other object in freefall, regardless of its horizontal velocity.
For example, a rock thrown horizontally from a 100.0 m high cliff at a velocity of 15.0 m/s will have its vertical motion equations used to calculate the time of fall and the vertical component of its velocity at impact, while the horizontal motion equation will be used to find the horizontal displacement at any point until impact.