Understanding the Concepts

* Gravitational Acceleration (g): The acceleration due to gravity is approximately 9.81 m/s², acting downwards.

* Conservation of Energy: The total mechanical energy (potential energy + kinetic energy) of the object remains constant throughout its motion (ignoring air resistance).

Steps to Solve

1. Initial Kinetic Energy:

* The initial kinetic energy (KE) of the mass is given by: KE = (1/2)mv²

* KE = (1/2)(0.800 kg)(30.0 m/s)² = 360 J (Joules)

2. Final Potential Energy:

* At its maximum height, the mass momentarily comes to rest (v = 0). Therefore, all its initial kinetic energy is converted into potential energy (PE).

* PE = mgh, where 'h' is the maximum height.

3. Equating Energy:

* Since energy is conserved: KE (initial) = PE (final)

* 360 J = (0.800 kg)(9.81 m/s²)h

4. Solving for Height:

* h = 360 J / [(0.800 kg)(9.81 m/s²)]

* h ≈ 45.9 m

Answer: The maximum height achieved by the mass is approximately 45.9 meters.