Final answer:
The horizontal distance D for the second rock thrown horizontally with an initial speed of 2v will be larger since the horizontal range is directly proportional to the initial horizontal speed, and both rocks are subject to the same gravitational acceleration.
Step-by-step explanation:
If the second rock is thrown horizontally off a cliff with an initial speed of 2v, as opposed to the initial speed v of the first rock, the horizontal distance D between the bottom of the cliff and the place where the rock lands will be larger. The horizontal distance a projectile travels is directly proportional to its initial horizontal speed, assuming no air resistance and that both rocks are subject to the same acceleration due to gravity.
Since gravity only affects the vertical motion of the rocks, and both rocks start from the same height, they will both take the same amount of time to reach the ground. However, the second rock, moving at an initial speed of 2v, will cover twice the horizontal distance in the same amount of time as the first rock, which was thrown with an initial speed v.
So, when comparing the landing spots, the second rock will hit the ground farther away from the cliff. Therefore, the claim is that the horizontal distance D will be larger for the second rock thrown with an initial speed of 2v.