Final answer:
The impact velocity of a rock thrown horizontally and thrown straight up at the same speed will be the same when it reaches ground level due to gravity affecting both objects equally and the conservation of energy.
Step-by-step explanation:
The impact velocities of a rock thrown horizontally off a cliff and thrown straight up from the cliff with the same initial speed will be the same when it reaches the same vertical position (e.g., ground level). This outcome occurs because the velocity of a falling object is determined only by its initial speed and vertical displacement, assuming acceleration due to gravity is the only force acting on it (gravity, vertical displacement).
In the case of the rock thrown horizontally from a height of 100.0 m with an initial speed of 15.0 m/s, the impact velocity is a combination of the initial horizontal velocity and the velocity acquired due to gravity during the fall. This will be the same as the speed at which it will hit if thrown straight upward with the same speed, irrespective of the direction of the throw. This is due to energy conservation principles where the kinetic energy at the point of release is transformed into potential energy at the apex of the throw (for the case of a rock thrown upwards), and then back into kinetic energy as it falls back down.