Final answer:
To calculate the speed of the pendulum ball, use the formula v = √(2 * g * L * (1 - cos(θ))), where L is the pendulum length, g is the gravitational acceleration, and θ is the angle from the vertical position of the pendulum.
Step-by-step explanation:
To calculate the speed of the ball in a pendulum, the correct formula to use when you have the frequency and the maximum angle is option a): v = √(2 * g * L * (1 - cos(θ))). This equation is derived from conservation of mechanical energy principles and leverages the gravitational constant g, the pendulum length L, and the cosine of the angle θ relative to the vertical. To find the speed at the bottom of the swing (when the string is vertically down), we simply plug in θ = 0° into this formula, which results in the maximum speed, as the entire potential energy at the release point has been converted into kinetic energy.