A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 2.90 s for the boat to travel from its highest point to its lowest, a total distance of 0.640 m. The fisherman sees that the wave crests are spaced 7.60 m apart.

How fast are the waves traveling?
V= m/s

What is the amplitude of each wave?
A=.320m

If the total vertical distance traveled by the boat were 0.400 m, but the other data remained the same, how fast are the waves traveling ?
v= m/s

If the total vertical distance traveled by the boat were 0.400 m, but the other data remained the same, what is the amplitude of each wave?
A=.2m

To find the speed of the waves, we can use the formula:

Speed = Distance / Time

Given that the distance between wave crests is 7.60 m and the time it takes for the boat to travel from the highest to the lowest point is 2.90 s, we can calculate the speed of the waves:

Speed = 7.60 m / 2.90 s
Speed = 2.62 m/s

Therefore, the speed of the waves is 2.62 m/s.

To find the amplitude of each wave, we can use the formula:

Amplitude = Total Distance / 2

Given that the total distance traveled by the boat is 0.640 m, we can calculate the amplitude of each wave:

Amplitude = 0.640 m / 2
Amplitude = 0.320 m

Therefore, the amplitude of each wave is 0.320 m.

If the total vertical distance traveled by the boat were 0.400 m, but the other data remained the same, we can calculate the new speed of the waves:

Speed = 7.60 m / 2.90 s
Speed = 2.62 m/s

Therefore, the speed of the waves would still be 2.62 m/s.

To find the new amplitude of each wave, we can use the formula:

Amplitude = Total Distance / 2

Given that the total distance traveled by the boat is now 0.400 m, we can calculate the new amplitude of each wave:

Amplitude = 0.400 m / 2
Amplitude = 0.200 m

Therefore, the new amplitude of each wave would be 0.200 m.

To find the speed of the waves, we can use the formula:

Speed = Distance / Time

In this case, the distance between two wave crests is given as 7.60 m and the time taken for the boat to travel from the highest point to the lowest point is 2.90 s. Therefore, we can substitute these values into the formula:

Speed = 7.60 m / 2.90 s

Calculating this, we find that the speed of the waves is approximately 2.624 m/s.

To find the amplitude of each wave, we need to know the total distance traveled by the boat from the highest point to the lowest point. In the given scenario, it is stated as 0.640 m. The amplitude of a wave is half of the total distance traveled.

So, Amplitude = Total Distance / 2

Plugging in the value:

Amplitude = 0.640 m / 2

Hence, the amplitude of each wave is 0.320 m.

Now, let's consider the case where the total vertical distance traveled by the boat is 0.400 m, but the other data remains the same.

Again, we can calculate the speed of the waves using the same formula:

Speed = 7.60 m / 2.90 s

This will still give us a value of approximately 2.624 m/s, as the speed of the waves does not depend on the vertical distance traveled by the boat.

To find the new amplitude of each wave, we use the formula we mentioned earlier:

Amplitude = Total Distance / 2

Plugging in the new value of total distance:

Amplitude = 0.400 m / 2

Therefore, the amplitude of each wave, in this case, is 0.200 m or 20 cm.