Final answer:
The question pertains to the motion of a stone thrown vertically upward from a cliff, a problem analyzed using physics kinematic equations. It includes finding the time to hit the ground, the maximum height reached, the velocity before impact, and the total distance traveled.
Step-by-step explanation:
The question involves a stone thrown vertically upward from a cliff and the study of its motion under gravity, which is a classic problem in physics. Using kinematic equations, we can analyze the motion in two parts: the ascent and the descent of the stone.
First, during the ascent, we find the maximum height the stone reaches above the cliff using the equation v^2 = u^2 + 2as, where v is the final velocity (0 m/s at the highest point), u is the initial speed (12 m/s), a is the acceleration due to gravity (-9.81 m/s^2, negative because it's in the opposite direction to the motion), and s is the displacement. Solving for s will give us the height above the cliff.
Subsequently, to calculate the total time it takes to reach the bottom, we use the two-motion equations: one for the upward motion until the stone stops, and another for the downward motion from the peak height above the cliff to the ground. The initial speed for the downward journey will be 0 m/s.
To calculate the velocity just before it hits the ground, we use the kinematic equation v^2 = u^2 + 2as. The initial speed is 0 m/s when the stone starts falling from the highest point, and s is the total distance between the highest point and the bottom of the cliff.
The total distance traveled by the stone will be the sum of the distance climbed above the cliff and the height of the cliff itself. For precision, kinematic equations are usually solved algebraically or with the aid of a calculator to ensure the accuracy of the answer, considering the influence of gravity which is constant at -9.81 m/s^2.