The boat will encounter a wave crest every 2 seconds while traveling west. The period of the waves hitting the boat will be equal to the period of the waves in the water.
Step-by-step explanation:
The period of a wave is the time taken for one complete cycle of the wave, which includes a crest and a trough. In this case, if the boat is traveling west, it will encounter a wave crest every time it reaches a distance equal to one wavelength from the previous crest. The speed of the boat will determine the time between two successive wave crests hitting the boat.
For example, if the speed of the boat is 10 meters per second and the wavelength of the waves is 20 meters, it will take the boat 2 seconds to travel a distance of 20 meters, which is the distance between two wave crests. Therefore, the boat will encounter a wave crest every 2 seconds while traveling west.
Comparing this time to the period of the waves in the water, we can see that the period of the waves hitting the boat will be equal to the period of the waves in the water, as both are determined by the wavelength and the speed of the waves.