If a coyote is standing at the top of a 125 m cliff getting ready to drop a 230 kg boulder on a road runner. What is the potential energy of the boulder just as he is ready to drop it? What is the kinetic energy of the boulder at the instant it hits the ground? How fast is the boulder going at the instant it hits the ground? I need a step by step formula for the questions and the answers.

Ep = mg*h = 230*9.8*125 = 281,750 Joules

Ek = Ep = 281,750 Joules.

V^2 = Vo^2 + 2g*h
V^2 = 0 + 19.6*125 = 2450
V = 49.5 m/s.

To solve these problems, we can use the principles of potential energy, kinetic energy, and conservation of energy. Here is a step-by-step guide on how to calculate the potential energy, kinetic energy, and velocity of the boulder:

1. Calculate the potential energy (PE) of the boulder at the top of the cliff:
- Potential energy is given by the equation PE = m * g * h, where
m is the mass of the object (230 kg),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
h is the height or vertical distance (125 m).
- Plug in the values: PE = 230 kg * 9.8 m/s^2 * 125 m.
- Calculate: PE = 284,750 Joules.

2. Calculate the kinetic energy (KE) of the boulder just before hitting the ground:
- The potential energy at the top of the cliff will convert into kinetic energy as the boulder falls.
- According to the law of conservation of energy, the total mechanical energy (potential energy + kinetic energy) remains constant.
Therefore, the kinetic energy just before hitting the ground will be equal to the potential energy at the top of the cliff.
- So, KE = 284,750 Joules.

3. Calculate the velocity (v) of the boulder just before hitting the ground:
- Kinetic energy is given by the equation KE = (1/2) * m * v^2, where
m is the mass of the object (230 kg),
v is the velocity of the object.
- Rearrange the equation to solve for v: v = sqrt((2 * KE) / m).
- Plug in the values: v = sqrt((2 * 284,750 Joules) / 230 kg).
- Calculate: v ≈ 20.81 m/s.

To summarize:
- The potential energy of the boulder just as it is ready to drop is 284,750 Joules.
- The kinetic energy of the boulder just before hitting the ground is also 284,750 Joules.
- The boulder will be traveling at approximately 20.81 m/s at the instant it hits the ground.

Please note that this calculation assumes there is no air resistance or friction involved in the scenario.