Final answer:
The time it takes for the stone to hit the water after being kicked off the cliff is approximately 3.2 seconds, as calculated using the kinematic equations of motion with constant acceleration due to gravity.
Step-by-step explanation:
The subject of this question is Physics, and it relates specifically to the topic of kinematics, which is part of classical mechanics. To determine how long it takes for the stone to hit the water, we use the following kinematic equation for an object under constant acceleration due to gravity (g = 9.8 m/s2):
d = vi * t + 0.5 * a * t2
In this scenario, the initial vertical velocity (vi) is 0 m/s since the stone is kicked horizontally over the edge. The distance (d) the stone falls is 52 m (the height of the cliff), and 'a' is the acceleration due to gravity. Plugging these values into the equation gives:
52 = 0 + 0.5 * 9.8 * t2
Solving for t, we get:
t2 = 52 / (0.5 * 9.8)
t2 = 52 / 4.9
t2 = 10.6122
t = √10.6122
t ≈ 3.26 seconds
However, this answer is not given in the options, so we round it to the closest answer which is option B) 3.2 seconds.