Final answer:
Both stones A and B will reach the ground at the same time when thrown horizontally from a cliff regardless of their differing initial speeds, because the time of fall is dependent only on the vertical distance and gravity.
Step-by-step explanation:
The time it takes for stone A and stone B to reach the ground when thrown horizontally from the top of a cliff is the same for both, regardless of their initial horizontal speeds. This is because the time of fall in a projectile motion only depends on the vertical distance and the acceleration due to gravity, which is constant at 9.8 m/s2. Horizontal motion and vertical motion are independent of each other when considering projectile motion without air resistance.
The horizontal velocity of these stones does not affect the time it takes to hit the ground because gravity acts only in the vertical direction. Thus, stone A with an initial speed of 15 meters per second and stone B with an initial speed of 30 meters per second will both reach the ground at the same time if they are dropped from the same height.