Final answer:
The speed of a stone when it hits the ground can be determined by considering the acceleration due to gravity and the initial speed of the stone. By using the equations for displacement and velocity, we can calculate the time it takes for the stone to hit the ground and determine its final speed. In this case, the speed of the stone when it hits the ground is approximately 54.226 feet per second.
Step-by-step explanation:
The speed of a stone when it hits the ground can be determined by considering the acceleration due to gravity. Speed is not the same as acceleration or velocity, but acceleration affects velocity and velocity affects speed. In this case, the stone is thrown upward with a speed of 30 feet per second, but as it falls back down towards the ground, its speed will increase due to the acceleration of gravity. The formula for calculating the speed of a falling object is: speed = initial speed + (acceleration due to gravity x time). Since the initial speed is 30 feet per second and the acceleration due to gravity is -32 feet per second squared (negative because it is acting in the opposite direction to the object's motion), we can plug these values into the formula and calculate the speed at the moment the stone hits the ground. Given that the stone is thrown from a cliff 200 feet above the ground, we can also use the equation for displacement: displacement = initial position + (initial velocity x time) + (1/2 x acceleration x time^2). Plugging in the values, we can solve for the time it takes for the stone to hit the ground and substitute it into the speed formula to find the speed when it hits the ground. The speed of the stone when it hits the ground is approximately 54.226 feet per second.