Final answer:
The height of the cliff from which a stone was dropped and hit the ground with a speed of 128 feet per second is calculated using the kinematic equation. It comes out to be approximately 254.4 feet.
Step-by-step explanation:
To find the height of the cliff from which a stone was dropped and hit the ground with a speed of 128 feet per second, we can use the kinematic equation:
v^2 = u^2 + 2gh
Where:
v = final velocity (128 feet per second)
u = initial velocity (0, since the stone was dropped)
g = acceleration due to gravity (32.2 feet per second squared)
h = height of the cliff (the value we are looking for)
Rearranging the equation to solve for h, we get:
h = (v^2 - u^2) / (2g)
Substituting in the known values:
h = (128^2 - 0^2) / (2 * 32.2)
h = 16384 / 64.4
h = 254.4 feet.
Therefore, the height of the cliff is approximately 254.4 feet.