Final answer:
The horizontal motion of the rock is described by the equation x = v₀t. The vertical motion is described by the equations y = y₀ + v₀t + 0.5gt² and v = v₀ + gt. The velocity at the point of impact can be calculated using the equation v = v₀ + gt.
Step-by-step explanation:
The equation that describes the horizontal motion of the rock thrown off a cliff is x = v₀t, where x is the horizontal displacement and v₀ is the initial horizontal velocity.
The equations that describe the vertical motion of the rock are y = y₀ + v₀t + 0.5gt² and v = v₀ + gt, where y is the vertical displacement, y₀ is the initial vertical position, v₀ is the initial vertical velocity, g is the acceleration due to gravity, and t is the time.
The rock's velocity at the point of impact can be calculated using the equation v = v₀ + gt, where v is the final velocity at the point of impact.