Final answer:
The radius of the wheel is equal to the amplitude of the given sinusoidal function describing the height of a nail on the wheel's circumference, which is 45 units.
Step-by-step explanation:
The height of a nail on the circumference of a wheel is described by the function f(t) = -45sin((1)/(20)t) + 60. This function is a sinusoidal function representing simple harmonic motion, which can be used to model the vertical motion of a point on the circumference of a rotating wheel. To determine the radius of the wheel, we need to understand the components of this function. The term -45sin((1)/(20)t) represents the sinusoidal oscillation, where the coefficient 45 is the amplitude of this sine wave. The radius of the wheel is equal to the amplitude of the sinusoidal function because this amplitude represents the maximum vertical displacement from the wheel's center, which occurs when the nail is at the top or bottom of the wheel. Therefore, the radius of the wheel is 45 cm (since the unit for radius is not given, we maintain the given numerical value).