Final answer:
The origin of the coordinate system is the initial position where the rock is thrown. The horizontal motion can be described by x = x0 + vxt, and the vertical motion can be described by y = y0 + v0yt - 0.5gt^2 and vy = v0y - gt. The velocity at the point of impact can be found using the Pythagorean theorem.
Step-by-step explanation:
(a) The origin of the coordinate system can be defined as the initial position where the rock is thrown horizontally off the cliff. It can be taken as the point where the rock is released.
(b) The horizontal motion of the rock can be described by the equation: x = x0 + vxt, where x is the distance traveled horizontally, x0 is the initial horizontal position, vx is the horizontal velocity, and t is the time.
(c) The vertical motion of the rock can be described by the equations: y = y0 + v0yt - 0.5gt2 and vy = v0y - gt, where y is the vertical position, y0 is the initial vertical position, v0y is the initial vertical velocity, g is the acceleration due to gravity, and t is the time.
(d) At the point of impact, the rock's velocity will have both horizontal and vertical components. The magnitude of the velocity can be found using the Pythagorean theorem: v = sqrt((vx)2 + (vy)2).