rock is thrown downward from the top of a cliff with an initial speed of 12 m/s, disregarding air resistance if the rock hits the ground after 2.0 s, what is the height of the cliff
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To find the height of the cliff, we need to use the kinematic equations of motion. Let's break down the problem step by step.
1. Identify the known values:
- Initial speed (u) = 12 m/s (upward)
- Acceleration (a) = acceleration due to gravity ≈ 9.8 m/s² (downward)
- Time (t) = 2.0 s
2. Determine the final velocity (v) at the time the rock hits the ground:
Since the rock is thrown downward, its final velocity will be negative, as it will be moving in the opposite (downward) direction. We can use the equation:
v = u + at
Plugging in the values:
v = 12 m/s + (-9.8 m/s²) * 2.0 s
v = 12 m/s - 19.6 m/s
v = -7.6 m/s
So, the final velocity of the rock when it hits the ground is -7.6 m/s.
3. Determine the initial height (h) of the rock:
We can use the equation:
h = ut + (1/2)at²
Plugging in the values:
h = (12 m/s) * 2.0 s + (1/2) * (-9.8 m/s²) * (2.0 s)²
h = 24 m - 19.6 m
h = 4.4 m
Therefore, the height of the cliff is 4.4 meters.