Understanding the Problem

* Neglecting Air Resistance: We'll assume there's no air resistance, which simplifies the problem.

* Conservation of Energy: The total mechanical energy (potential energy + kinetic energy) of the baseball remains constant throughout its flight.

Solution

1. Initial Kinetic Energy: The baseball starts with only kinetic energy:

* KE₁ = (1/2) * m * v₁²

* where:

* KE₁ is the initial kinetic energy

* m is the mass of the baseball

* v₁ is the initial velocity (150 m/s)

2. Final Kinetic Energy: When the ball hits the ground, all its potential energy has been converted back into kinetic energy. Since energy is conserved, the final kinetic energy (KE₂) equals the initial kinetic energy (KE₁).

3. Final Velocity:

* KE₂ = (1/2) * m * v₂²

* Since KE₁ = KE₂, we have: (1/2) * m * v₁² = (1/2) * m * v₂²

* Notice that the mass (m) cancels out.

* Solving for v₂ (the final velocity): v₂ = √(v₁²) = v₁

Answer

The speed of the baseball when it hits the ground will be 150 m/s.

Important Note: This assumes no air resistance. In reality, air resistance would slow the ball down, resulting in a slightly lower final velocity.