Final answer:
To determine how often a powerboat encounters a wave crest, the relative speed of the boat to the crests must be calculated, and then used along with the wavelength to determine the frequency of encounters. If waves have a propagation speed of 5.00 m/s and wavelength of 40.0 m, the powerboat encounters a wave crest approximately 18 times per minute.
Step-by-step explanation:
To calculate how often a powerboat encounters a wave crest while moving at 17 m/s relative to the ocean floor, we'd need to determine the wave frequency that is, the number of crests passing a fixed point per second. Given that the boat is traveling west, if it encounters wave crests that are moving in the same or the opposite direction, their relative speeds will be different.
If the waves are moving in the same direction as the boat and assuming that the waves have the same properties as those mentioned which have a propagation speed of 5.00 m/s, then the relative speed at which the boat encounters the crests would be the boat's speed minus the wave speed (17 m/s - 5.00 m/s = 12 m/s). If the wavelength of the waves is 40.0 m, we can find the frequency with which the boat encounters wave crests by dividing the relative speed by the wavelength.
Frequency of encounter = Relative speed / Wavelength = 12 m/s / 40.0 m = 0.3 encounters per second. To find out how often this happens in a minute, we multiply by 60 seconds.
0.3 encounters/s * 60 s/min = 18 encounters per minute.