To solve this problem, we can analyze the horizontal and vertical motions of the stone separately.
First, let's consider the vertical motion of the stone. We can use the equation for vertical displacement in free fall:
y = ut + (1/2)gt^2
where: y = vertical displacement (200 m in this case, the height of the cliff) u = initial vertical velocity (0 m/s since the stone was only kicked horizontally) t = time taken g = acceleration due to gravity (approximately 9.8 m/s^2)
Plugging in the values, we get:
200 = 0*t + (1/2)9.8t^2 200 = 4.9t^2
Simplifying the equation:
t^2 = 200/4.9 t^2 = 40.8163265
Taking the square root of both sides:
t ≈ √40.8163265 t ≈ 6.39 seconds (rounded to two decimal places)
Therefore, it takes approximately 6.39 seconds for the stone to reach the ground.
Now, let's consider the horizontal motion of the stone. The horizontal velocity remains constant at 9 m/s throughout the stone's flight. So, to find the horizontal distance traveled, we can use the equation:
distance = velocity * time
distance = 9 m/s * 6.39 s distance ≈ 57.51 meters (rounded to two decimal places)
Therefore, the stone will hit the ground approximately 57.51 meters away from the base of the cliff.