Final answer:
The height the golf ball will reach when the spring is released is approximately 1.02 meters.
Step-by-step explanation:
To determine the height the golf ball will reach when the spring is released, we can use the principle of conservation of energy. When the spring is compressed, it contains potential energy, which is converted to kinetic energy when released. This kinetic energy is then converted to gravitational potential energy as the ball reaches its highest point.
Using the formula for potential energy, we can calculate the height:
PE = m * g * h
Where PE is the potential energy, m is the mass of the golf ball, g is the acceleration due to gravity (9.8 m/s²), and h is the height.
By equating the potential energy to the initial kinetic energy, we have:
0.5 * k * x² = m * g * h
Where k is the spring constant and x is the compression distance.
Substituting the given values:
0.5 * 200 N/m * 0.0500 m² = 0.0250 kg * 9.8 m/s² * h
Simplifying the equation, we find that the height h is approximately 1.02 m.