Two people are fishing from small boats located 28 m apart.Waves pass through the water,
and each person’s boat bobs up and down 15 times in 1.0 min. At a time when one boat is on a
crest, the other one is in a trough, and there is one crest between the two boats. What is the
speed of the waves?
the boats are 1.5 wave lengths apart ... crest to crest to trough
wavelength = 28 m / 1.5 cycle
frequency = 15 cycles / 1.0 min
wave speed = wavelength * frequency
Well, I have to say, those boats really know how to bust a move on those waves! It sounds like they're having a whale of a time out there. Anyway, let's calculate the speed of those waves.
We know that when one boat is on a crest, the other boat is in a trough, and there is one crest between them. So, the distance between the crest and the trough is 28 meters (the distance between the boats).
Now, we also know that each boat bobs up and down 15 times in 1.0 minute. This means that in one minute, the wave travels a distance equal to 2 crests and 2 troughs, or 30 meters (15 crests + 15 troughs).
Therefore, the speed of the waves can be calculated by dividing the total distance traveled by the time it takes, which is 30 meters / 1.0 minute.
So, it seems like those wavy waves are cruising along at a speed of 30 meters per minute. Have a fin-tastic day!
To find the speed of the waves, we need to determine the wavelength of the waves and the time it takes for one complete wave to pass through the two boats.
Let's start by determining the wavelength.
Given:
Distance between the two boats (d) = 28 m
Number of crests between the two boats (n) = 1
The wavelength (λ) can be calculated using the formula:
λ = d / n
Substituting the given values, we get:
λ = 28 m / 1
λ = 28 m
Now, let's determine the time it takes for one complete wave to pass through the two boats.
Given:
Number of waves per minute (f) = 15 waves/min
Time taken for one wave to pass (T) = 1 / f
Substituting the given value, we get:
T = 1 min / 15
T = 0.067 min
We need to convert this time to seconds since the speed of waves is usually given in meters per second.
T = 0.067 min * 60 s/min
T ≈ 4.0 s
Finally, we can calculate the speed of the waves using the formula:
v = λ / T
Substituting the values we found earlier, we get:
v = 28 m / 4.0 s
v ≈ 7.0 m/s
Therefore, the speed of the waves is approximately 7.0 m/s.
To find the speed of the waves, we need to determine the wavelength and the period of the waves.
In this scenario, we are given that each boat bobs up and down 15 times in 1.0 minute. We can use this information to calculate the period of the waves.
The period of a wave is the time it takes for one complete wave cycle. Since one complete wave cycle consists of a crest and a trough, and each boat bobs up and down 15 times, we can say that the period is the time it takes for one boat to complete 15 bobbing motions.
Therefore, the period (T) is given by:
T = 1.0 min / 15
T ≈ 0.067 min
Now, we can calculate the wavelength (λ) using the given information that there is one crest between the two boats.
The wavelength is the distance between two consecutive crests (or troughs). In this case, since there is one crest between the two boats, the distance between the boats is equal to one wavelength.
Thus, the wavelength (λ) is given by:
λ = 28 m
Finally, we can calculate the speed (v) of the waves using the formula:
v = λ / T
v = 28 m / 0.067 min
Remember to convert the time to seconds before performing the calculation:
v = 28 m / (0.067 min * 60 s/min)
v ≈ 66.27 m/s
Therefore, the speed of the waves is approximately 66.27 m/s.