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
Your amplitudes are right... but for how fast, they want a numerical value. (Sorry, I can't help with that.)
To find the speed (V) of the waves, we can use the formula:
V = λ / T
where λ represents the wavelength (distance between wave crests) and T represents the period (time for one complete oscillation).
In this case, the wavelength (λ) is given as 7.60 m and the period (T) is given as 2.90 s.
Therefore, we can substitute these values into the formula:
V = 7.60 m / 2.90 s
Simplifying the equation gives us:
V ≈ 2.62 m/s
Hence, the waves are traveling at approximately 2.62 m/s.
To find the amplitude (A) of each wave, we need to halve the total distance traveled by the boat (0.640 m) since the boat moves from the highest to the lowest point, which represents half the wavelength.
Therefore, the amplitude is:
A = 0.640 m / 2
A ≈ 0.320 m
So, the amplitude of each wave is approximately 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 (v) of the waves using the same formula as before:
v = λ / T
The wavelength (λ) remains 7.60 m, and the new total vertical distance traveled by the boat is 0.400 m.
Thus, substituting these values into the formula gives us:
v = 7.60 m / 2.90 s
v ≈ 2.62 m/s
Therefore, the speed of the waves remains approximately 2.62 m/s.
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 amplitude (A) of each wave.
Since the amplitude is half the total vertical distance traveled by the boat, the amplitude would be:
A = 0.400 m / 2
A ≈ 0.200 m
Thus, the amplitude of each wave would be approximately 0.200 m.