Understanding the Concepts

* Potential Energy: An object gains potential energy when it's lifted against gravity. The formula is: PE = mgh, where:

* PE = Potential energy (in Joules)

* m = mass (in kg)

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

* h = height (in meters)

* Kinetic Energy: An object possesses kinetic energy due to its motion. The formula is: KE = (1/2)mv², where:

* KE = Kinetic Energy (in Joules)

* m = mass (in kg)

* v = velocity (in m/s)

* Conservation of Energy: In the absence of air resistance, the total mechanical energy (potential energy + kinetic energy) of a system remains constant.

Solving the Problem

1. Calculate Potential Energy:

* PE = mgh = (1 kg)(9.8 m/s²)(20 m) = 196 Joules

2. Initial Kinetic Energy:

* Since the object starts at rest and reaches a height of 20 meters, its initial kinetic energy is converted entirely into potential energy at the highest point.

* Therefore, the initial kinetic energy (KE) is equal to the potential energy (PE): KE = 196 Joules

3. Calculate Initial Velocity:

* KE = (1/2)mv²

* 196 Joules = (1/2)(1 kg)v²

* v² = 392

* v = √392 ≈ 19.8 m/s

Answer:

* The initial velocity that must be given to the 1 kg mass is approximately 19.8 m/s.

* The total energy of the system is 196 Joules, which remains constant throughout the motion (ignoring air resistance).