Seafaring mariners report that in great storms when the average peak$-$to$-$peak wave height becomes about $1/7$ of the wavelength, the tops of the largest ocean waves can become separated from the rest of the wave. They claim that the wind and the wave's forward velocity cause huge "hunks" of water to tumble down the face of the wave. Some are reportedly large enough to damage or capsize small vessels. The analytic expression for the vertical displacement of the water surface when an ocean wave of amplitude A is propagating in the $+$x direction is z$($x$,$t$)=$Acos$($kx$$t$).$ Now find the critical ratio of A to such that this wave will have a maximum acceleration at the top of $$g$.$ Then the water at the top would have to accelerate faster than g to stay connected with the wave, which is clearly not possible!