A stone was dropped off a cliff and hit the ground with a speed of 152 ft/s. What is the height of the cliff? (Use 32 ft/s2 for the acceleration due to gravity.)Part 1 of 4We know that s(t) = 12at2 + v0t + s0. In this situation, we have a = ft/s2, v0 = ft/s, and s0 = h, where h is the height of the cliff (in feet) that we wish to find.
Question
A stone was dropped off a cliff and hit the ground with a speed of 152 ft/s. What is the height of the cliff? (Use 32 ft/s2 for the acceleration due to gravity.)Part 1 of 4We know that s(t) = 12at2 + v0t + s0. In this situation, we have a = ft/s2, v0 = ft/s, and s0 = h, where h is the height of the cliff (in feet) that we wish to find.
Solution
In this problem, we are given the final velocity (v) of the stone when it hits the ground, which is 152 ft/s. We are also given the acceleration due to gravity (a), which is 32 ft/s². The initial velocity (v0) of the stone is 0, because the stone was dropped, not thrown. The initial height (s0) is what we are trying to find.
We can use the equation of motion that relates final velocity, initial velocity, acceleration, and displacement:
v² = v0² + 2as
Substituting the given values into the equation:
(152 ft/s)² = (0 ft/s)² + 2*(32 ft/s²)*s
Solving for s (which represents the height of the cliff):
s = ((152 ft/s)² - (0 ft/s)²) / (2*(32 ft/s²))
s = (23104 ft²/s²) / (64 ft/s²)
s = 361 ft
So, the height of the cliff is 361 feet.
Similar Questions
We know that s(t) = 12at2 + v0t + s0. In this situation, we have a = ft/s2, v0 = ft/s, and s0 = h, where h is the height of the cliff (in feet) that we wish to find.
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