Understanding the Concepts

* Kinetic Energy (KE): The energy an object possesses due to its motion. It's calculated as KE = (1/2) * m * v^2, where:

* m = mass of the object

* v = velocity of the object

* Potential Energy (PE): The energy an object possesses due to its position relative to a reference point. For objects near the Earth's surface, PE = m * g * h, where:

* m = mass of the object

* g = acceleration due to gravity (approximately 9.8 m/s²)

* h = height above the reference point

Solution

1. Conservation of Energy: As the rock falls, its potential energy (PE) is converted into kinetic energy (KE). Therefore, we can say:

PE (at height) = KE (at ground)

m * g * h = (1/2) * m * v^2

2. Solving for Velocity: We need to find the velocity (v) of the rock just before it hits the ground. We can rearrange the conservation of energy equation to solve for v:

v² = 2 * g * h

v = √(2 * g * h)

v = √(2 * 9.8 m/s² * 10 m)

v ≈ 14 m/s

3. Calculating Mass: Now that we know the velocity, we can use the kinetic energy formula to solve for the mass:

KE = (1/2) * m * v²

33000 J = (1/2) * m * (14 m/s)²

m = (2 * 33000 J) / (14 m/s)²

m ≈ 33.9 kg

Therefore, the mass of the rock is approximately 33.9 kg.