Final answer:
Boats in the harbor are most protected against wave action at angles where the diffraction of waves creates areas of minimum wave intensity. This angle is related to the first minimum of the diffraction pattern, but the exact calculation requires applying the principles of wave physics.
Step-by-step explanation:
The question pertains to the phenomenon known as diffraction, which occurs when waves encounter an obstacle or slit that is comparable in size to their wavelength.
In the given scenario, ocean waves with a wavelength of 20.0 meters approach a 50.0-meter wide opening in a rock barrier at a harbor's entrance. The protection against wave action inside the harbor depends on the angle at which diffraction occurs.
According to the principles of wave diffraction, the angle of maximum protection, or where the intensity of waves is greatly reduced, is where the first minimum of wave intensity would occur past the opening. This can be calculated using the formula for the angle θ for the first minimum of a single-slit diffraction pattern given by θ = sin-1(λ/d), where λ is the wavelength and d is the width of the opening.
However, the angle for the fifth maximum can be found using the modified condition for maxima mλ = d sin(θ), where m is the order number of the maximum. Although the exact calculation for the first minimum is not provided, it can be deduced that the boats inside the harbor are most protected at angles beyond this first minimum of wave intensity.
In practical terms, boats would be safest in a direction that forms a greater angle with the incident wave direction, beyond the point where the waves begin to spread out or 'fan out' after passing through the opening. The precise calculation requires knowledge of wave physics and involves understanding diffraction patterns.