Answer:
1.869 hours
Explanation:
[tex]T[/tex] = Time period = 11.1 h
Angular frequency is given by
[tex]\omega=\frac{2\pi}{T}\\\Rightarrow \omega=\frac{2\pi}{11.1}\\\Rightarrow \omega=0.566\ rad/h[/tex]
The distance moved from highest to lowest level is given by
[tex]d=2x_{m}\\\Rightarrow x_m=\frac{d}{2}\\\Rightarrow x_m=0.5d[/tex]
At the ocean surface [tex]x_m=0.25d[/tex]
[tex]x=x_mcos(\omega t+\phi)[/tex]
[tex]\phi[/tex] = Phase constant = 0 as clock is started at [tex]x_0=x_m[/tex]
[tex]0.25d=0.5dcos(0.56t)\\\Rightarrow cos(0.56t)=\frac{0.25}{0.5}\\\Rightarrow 0.56t=cos^{-1}0.5\\\Rightarrow t=\frac{1.047}{0.56}\\\Rightarrow t=1.869\ h[/tex]
The time taken for the water to fall the distance is 1.869 hours