Final answer:
The work-energy principle can be used to find the rock's speed just as it leaves the ground, and the rock's maximum height can be calculated using the work done against gravity. By substituting the given values into the equations, the rock's speed just as it leaves the ground can be determined, and the maximum height it reaches is found to be approximately 19.3m.
Step-by-step explanation:
The work-energy principle states that the work done on an object is equal to its change in kinetic energy. In this case, we can use this principle to find the rock's speed just as it leaves the ground.
First, we can calculate the work done on the rock to reach a height of 12m. The work done is equal to the change in kinetic energy, which is given by the equation:
Work = change in kinetic energy = (1/2) * mass * (final velocity^2 - initial velocity^2)
Since the rock is traveling upward at 17m/s when it reaches 12m high, we can write the equation as:
Work = (1/2) * 11n * (17^2 - 0^2)
Simplifying this equation gives:
Work = 2047.5n
We can then use the work-energy principle to find the rock's speed just as it leaves the ground. The work done on the rock is equal to the work done against gravity, which is given by the equation:
Work = force * distance = m * g * h
where m is the mass of the rock, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height the rock is thrown from.
Substituting the given values into the equation, we have:
2047.5n = 11n * 9.8m/s^2 * h
Simplifying this equation gives:
h = 2047.5 / (11 * 9.8)
h ≈ 19.3m
Therefore, the rock's maximum height is approximately 19.3m.