A fisherman notices that his boat is moving up and down periodically rowing to waves on the surface of the water. It takes 3.0 seconds for the boat to travel from its highest point to it's lowest, a total distance of 0.800m. The fisherman sees that the wave crests are spaced 8.0m apart. What is the speed of the water waves?
wavelength=16m f=1/6sec A=.4m
f*lambda=speed
crest to trough (half wavelength) time is 3.0 s , so 6.0 s for a full wavelength
the wavelength is 8.0 m
wave speed is ... 8.0 m / 6.0 s
To find the speed of the water waves, we can use the formula: speed = distance/time.
In this case, the distance between two wave crests is given as 8.0 m, and the time it takes for the boat to travel from its highest point to its lowest is 3.0 seconds. However, we need to find the speed of the waves, not the speed of the boat.
Since the boat moves up and down with the waves, the distance it covers in one full cycle (from highest to lowest point and back to the highest) is twice the distance between wave crests. So, the total distance traveled by the boat in one complete cycle is 2 * 8.0 m = 16.0 m.
Now, we can use the formula to calculate the speed of the water waves:
speed = distance/time = 16.0 m / 3.0 s
Calculating this, we find that the speed of the water waves is approximately 5.33 m/s.