Final answer:
To find the speed of the waves affecting the fisherman's boat, we use the wave speed formula with a frequency of 0.2Hz and a wavelength of 4.8m, obtaining a wave speed of 0.96m/s.
Step-by-step explanation:
In order to calculate the speed of the waves that the fisherman is experiencing, we need to use the wave speed formula v = λf, where v represents the wave speed, λ is the wavelength, and f is the frequency. Given that the distance between wave crests (wavelength) is 4.8m and the boat takes 5 seconds to complete one full cycle (from the peak, down to the trough, and back up to the peak again), the frequency is 1/5 Hz, because frequency is the number of cycles per second.
To calculate the frequency more accurately, we actually need to divide the total cycle time by 2, since the boat takes 2.5s to go from the highest point to the lowest, and will take another 2.5s to return to the highest point, making a complete cycle 5s. Therefore, the frequency (f) is 1 cycle per 5 seconds or 0.2Hz.
Now we can find the wave speed (v) by plugging into the formula: v = λf = 4.8m × 0.2Hz = 0.96m/s. Hence, the waves are traveling at a speed of 0.96 meters per second.