At time \(t\) hours after a high tide, the height, \(h\) metres, of the tide and the velocity, \(v\) knots, of the tidal flow can be modelled using the parametric equations
$$\begin{aligned}
& v = 4 - \left( \frac { 2 t } { 3 } - 2 \right) ^ { 2 }
& h = 3 - 2 \sqrt [ 3 ] { t - 3 }
\end{aligned}$$
High tides and low tides occur alternately when the velocity of the tidal flow is zero.
A high tide occurs at 2 am.
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Use the model to find the height of this high tide.
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(ii) Find the time of the first low tide after 2 am.
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(iii) Find the height of this low tide.
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Use the model to find the height of the tide when it is flowing with maximum velocity.
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