Question

You throw a 3.00 N rock vertically into the air from ground level. You observe that when it is 14.0 m above the ground, it is traveling at 24.0 m/s upward. Use the work-energy theorem to find its maximum height. Express your answer with the appropriate units.

Answer 1

To find the maximum height of the rock, we can use the work-energy theorem. The work done on the rock is equal to its change in potential energy. The maximum height of the rock is found to be 0.306 m.

Step-by-step explanation:

To find the maximum height of the rock, we can use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In this case, the rock is thrown vertically, so the work done on the rock is equal to its change in potential energy. We can calculate the work done on the rock by multiplying the force applied (which is equal to the weight of the rock, 3.00 N) by the distance traveled (which is equal to the maximum height, h).

The work done on the rock is given by W = F * d, where W is the work done, F is the force applied, and d is the distance traveled. Therefore, W = 3.00 N * h = 3.00h Joules. This work is equal to the change in potential energy, so we can write W = m * g * h, where m is the mass of the rock and g is the acceleration due to gravity. For simplicity, we can assume that the mass of the rock cancels out, so we have 3.00h = g * h. Solving for h, we find that the maximum height of the rock is h = 3.00 / g. Using the value of g = 9.8 m/s^2, we can calculate h = 0.306 m.