The rock reaches a maximum height of 20.4 m above the top of the cliff before falling to the base of the cliff, landing 5.56 s after it was thrown. How high is the cliff?
To determine the height of the cliff, we need to use the equation of motion for an object in free fall.
The equation is given by:
h = (1/2) * g * t^2
Where:
h is the height of the object
g is the acceleration due to gravity (9.8 m/s^2 on Earth)
t is the time in seconds
In this case, we are given the time it takes for the rock to hit the base of the cliff, which is 5.56 seconds. We also know that the rock reaches a maximum height of 20.4 m above the top of the cliff.
Let's use this information to find the height of the cliff:
1. First, we need to find the time it takes for the rock to reach its maximum height. Since the total time is 5.56 seconds and the rock spends an equal amount of time on its ascent and descent, the time to reach the maximum height is half of the total time, which is t = 5.56/2 = 2.78 seconds.
2. Now, we can use the equation of motion to find the height at that time:
h = (1/2) * g * t^2
h = (1/2) * 9.8 * (2.78)^2
h ≈ 38.6584 m
3. However, this is the height above the top of the cliff, not the height of the cliff itself. To find the height of the cliff, we need to subtract the initial height of the rock from the maximum height. Since the maximum height is 20.4 m above the top of the cliff, the height of the cliff is h - 20.4:
Height of the cliff = 38.6584 - 20.4 = 18.2584 m
Therefore, the height of the cliff is approximately 18.2584 meters.