Answer:
The time elapses until the boat is first at the trough of a wave is 4.46 seconds.
Explanation:
Speed of the wave, v = 59 km/h = 16.38 m/s
Wavelength of the wave, [tex]\lambda=145\ m[/tex]
If f is the frequency of the wave. The frequency of a wave is given by :
[tex]v=f\lambda\\\\f=\dfrac{v}{\lambda}\\\\f=\dfrac{16.38\ m/s}{145\ m}\\\\f=0.112\ Hz[/tex]
The time period of the wave is given by :
[tex]T=\dfrac{1}{f}\\\\T=\dfrac{1}{0.112\ Hz}\\\\T=8.92\ s[/tex]
We need to find the time elapses until the boat is first at the trough of a wave. So, the time will be half of the time period of the wave.
[tex]T=\dfrac{8.92}{2}\\\\T=4.46\ s[/tex]
Hence, this is the required solution.
