Final answer:
The horizontal distance from the base of the cliff where the stone lands is approximately 126.9 m.
Step-by-step explanation:
To find the horizontal distance from the base of the cliff where the stone lands, we need to use the formula for horizontal displacement: d = v*t. In this case, the initial velocity in the horizontal direction (v) is equal to the horizontal component of the stone's initial velocity, which is the same as its horizontal speed. So, v = 86.3 m/s. The time (t) it takes for the stone to land can be found using the equation for free-fall motion: t = sqrt(2h/g), where h is the initial vertical height of the cliff and g is the acceleration due to gravity. Plugging in the values h = 10.6 m and g = 9.8 m/s^2, we find t ≈ 1.47 s. Now, we can calculate the horizontal distance: d = v*t = 86.3 m/s * 1.47 s ≈ 126.9 m.