Final answer:
The velocity of a ball at half the maximum height relative to the equilibrium point of a spring can be found using conservation of energy principles, where the kinetic energy at the midpoint is calculated from the potential energy at that point, given the ball's mass.
Step-by-step explanation:
The question is related to finding the ball's velocity at half of the maximum height during its motion when released from a spring. Assuming the question is based on the conservation of mechanical energy and ignores air resistance, we know that the total mechanical energy of the system (potential and kinetic) is conserved. We can calculate potential energy at the equilibrium point and at the maximum height, and use these values to find the kinetic energy, and hence the velocity, at the midpoint.
To solve a similar problem, one could use the formula KE = 0.5 * mv2, where KE is kinetic energy, m is mass, and v is velocity. The potential energy at the point of release would be equal to the kinetic energy at the midpoint (ignoring any other forces).
Example: If the ball had a potential energy of 100 J at the maximum height, at the midpoint, the potential energy would be 50 J. If the mass of the ball was 2 kg, we would find the velocity at the midpoint by setting KE = 50 J. Therefore, 0.5 * 2 kg * v2 = 50 J, solving for v gives us 5 m/s.