Final answer:
The potential energy at the highest point of a golf ball, initially moving at 30.0 m/s, is equivalent to its initial kinetic energy. The calculated value is 20.25 J, assuming the mass of the ball is the standard 0.045 kg, which does not match any of the provided answer choices.
Step-by-step explanation:
The question is asking to find the potential energy of a golf ball at its highest point after given an initial speed of 30.0 m/s. Assuming that we are dealing with a frictionless environment and no air resistance, we can apply the conservation of mechanical energy principle to solve this.
We know that at the highest point of its trajectory, the ball's kinetic energy will be 0 because its velocity will be 0. All of the initial kinetic energy will have been converted into potential energy. To calculate the potential energy at the highest point, we use the initial kinetic energy, which is given by the formula KE = (1/2)mv², where m is the mass of the ball and v is the initial speed.
The mass of the golf ball is not given, but for the sake of this calculation, we can assume it to be 0.045 kg (the standard mass of a golf ball). Inserting the values into the formula, we get KE_initial = (1/2)(0.045 kg)(30.0 m/s)² = 20.25 J. Because energy is conserved, this kinetic energy becomes the potential energy (PE) at the highest point.
However, with the values given, none of the multiple-choice answers (45 J, 90 J, 135 J, 180 J) match the calculated KE_initial of 20.25 J. Therefore, based on the calculation, it seems that there may be an error in the given options or an assumption such as the mass of the golf ball may differ from the standard.