A rock falls off the edge of a cliff and strikes the ground after 3.8 s. What is the height of the cliff? Assume air resistance is negligible
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Use the formula:
h = vo*t - (1/2)gt^2
Since the rock experiences freefall, initial velocity (vo) is zero:
h = -(1/2)gt^2
Substitute:
h = -(1/2)(-9.8)(3.8^2)
h = ?
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To determine the height of the cliff, we can use the equations of motion for free-falling objects.
The key equation we will use is:
h = (1/2) * g * t^2,
where:
- h is the height of the cliff,
- g is the acceleration due to gravity (which is approximately 9.8 m/s^2 on Earth),
- t is the time it takes for the rock to fall.
In this case, we are given the time it takes for the rock to fall, which is 3.8 seconds. We can substitute this value into the equation to find the height of the cliff.
h = (1/2) * 9.8 * (3.8)^2
= 0.5 * 9.8 * 14.44
≈ 70.588 meters.
Therefore, the height of the cliff is approximately 70.588 meters.