Question

Suppose high tide is at midnight, the water level at midnight is 3 m, and the water level at low tide is 0.5 m. Assuming the next high tide will occur 12 hours later (at noon), find the time, to the nearest minute, when the water level is at 1.125 m for the second time after midnight.

Answer 1

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

$t=10.0hours$

From the Question we are told that

Maximum height $h_{max}=3m$

Minimum height  $H_{min}=0.5m$

Time for  next high tide will occur$T=12 hours =>720 min$

Generally Average Height

$h_{avg}=\frac{3+0.5}{2}\\\\h_{avg}=1.75$

Therefore determine Amplitude to be

$A=h_{max}=j_{avg}\\\\A=3-1.75\\\\A=1.25$

Generally, the equation for Time is mathematically given by

At t=0

$h(x)=Acos(Bx)+h_{avg}$

Where

$B=\frac{2\pi}{P}\\\\B=\frac{2\pi}{720}\\\\B=8.73*10^{-3}$

Therefore

$h(t)=Acos8.73*10^{-3}(t)+h_{avg}$

Hence the Time at $T=1.125$ is

$1.125(t)=1.25cos(8.73*10^{-3})(t)+1.75$

$-0.1249t=1.75$

$t=10.0hours$

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