Understanding the Concepts
* Potential Energy: The energy an object possesses due to its position. For an object at a height, potential energy (PE) is calculated as: PE = mgh (where m is mass, g is acceleration due to gravity, and h is height).
* Kinetic Energy: The energy an object possesses due to its motion. Kinetic energy (KE) is calculated as: KE = (1/2)mv² (where m is mass and v is velocity).
* Conservation of Energy: In a closed system, the total energy remains constant. This means potential energy can be converted into kinetic energy, and vice versa.
Solving the Problem
1. Initial Energy: At the starting height, the ball has only potential energy:
PE = mgh = (0.3 kg)(9.8 m/s²)(8 m) = 23.52 J (Joules)
2. Final Energy: Just before hitting the ground, the ball has only kinetic energy:
KE = (1/2)mv²
3. Conservation of Energy: The initial potential energy is equal to the final kinetic energy:
PE = KE
23.52 J = (1/2)(0.3 kg)v²
4. Solving for Velocity (v):
* 23.52 J = 0.15 kg * v²
* v² = 23.52 J / 0.15 kg = 156.8 m²/s²
* v = √156.8 m²/s² ≈ 12.5 m/s
Answer: The ball is going approximately 12.5 m/s when it hits the ground. So the closest answer is B. 12.5.
