Ocean waves are traveling to the east at 4 m/s with a distance of 20m between crests. With what frequency do the waves hit the front of a boat (a) when the boat is at anchor and (b) when the boat is moving westward at 1 m/s?

frequency= distance/velocity

For the second, the relative veloicty is faster, 5 m/s.

a) When the boat is at anchor, the frequency at which the waves hit the boat is the same as the frequency of the waves themselves. So, we can use the formula:

frequency = velocity/distance = 4 m/s / 20 m = 0.2 Hz

b) When the boat is moving westward at 1 m/s, the relative velocity between the boat and the waves increases to 5 m/s. So, we can use the formula:

frequency = relative_velocity/distance = 5 m/s / 20 m = 0.25 Hz

(a) When the boat is at anchor, the frequency with which the waves hit the front of the boat can be calculated using the equation:

frequency = distance / velocity

Given that the distance between crests is 20 m and the waves are traveling to the east at 4 m/s, the frequency is:

frequency = 20 m / 4 m/s
frequency = 5 Hz

Therefore, when the boat is at anchor, the waves hit the front of the boat at a frequency of 5 Hz.

(b) When the boat is moving westward at 1 m/s, the relative velocity between the boat and the waves becomes 5 m/s (4 m/s - 1 m/s).

Using the same formula:

frequency = distance / velocity

The frequency with which the waves hit the front of the moving boat is:

frequency = 20 m / 5 m/s
frequency = 4 Hz

Therefore, when the boat is moving westward at 1 m/s, the waves hit the front of the boat at a frequency of 4 Hz.

To calculate the frequency of the waves hitting the front of the boat, we need to use the formula: frequency = distance / velocity.

(a) When the boat is at anchor, the velocity of the waves is 4 m/s to the east, and the distance between each crest (wavelength) is 20 meters. So, the frequency can be calculated as:

frequency = 20 meters / 4 m/s = 5 Hz

Therefore, when the boat is at anchor, the waves will hit the front of the boat with a frequency of 5 Hz.

(b) When the boat is moving westward at 1 m/s, the relative velocity between the boat and the waves is the sum of their individual velocities. In this case, the waves are still moving to the east at 4 m/s, and the boat is moving westward at 1 m/s. Therefore, the relative velocity is 4 m/s + (-1 m/s) = 3 m/s.

Using the same wavelength of 20 meters, we can calculate the frequency as:

frequency = 20 meters / 3 m/s = 6.67 Hz

Therefore, when the boat is moving westward at 1 m/s, the waves will hit the front of the boat with a frequency of approximately 6.67 Hz.