Respuesta :
We have that the time, to the nearest minute, when the water level is at 1.125 m for the second time after midnight is
[tex]t=10.0hours[/tex]
From the Question we are told that
Maximum height [tex]h_{max}=3m[/tex]
Minimum height [tex]H_{min}=0.5m[/tex]
Time for next high tide will occur[tex]T=12 hours =>720 min[/tex]
Generally Average Height
[tex]h_{avg}=\frac{3+0.5}{2}\\\\h_{avg}=1.75[/tex]
Therefore determine Amplitude to be
[tex]A=h_{max}=j_{avg}\\\\A=3-1.75\\\\A=1.25[/tex]
Generally, the equation for Time is mathematically given by
At t=0
[tex]h(x)=Acos(Bx)+h_{avg}[/tex]
Where
[tex]B=\frac{2\pi}{P}\\\\B=\frac{2\pi}{720}\\\\B=8.73*10^{-3}[/tex]
Therefore
[tex]h(t)=Acos8.73*10^{-3}(t)+h_{avg}[/tex]
Hence the Time at [tex]T=1.125[/tex] is
[tex]1.125(t)=1.25cos(8.73*10^{-3})(t)+1.75[/tex]
[tex]-0.1249t=1.75[/tex]
[tex]t=10.0hours[/tex]
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