8 The height of tide at the entrance to a harbour on a particular day may be modelled by the function \(h = 3 + 2 \sin 30 t + 1.5 \cos 30 t\) where \(h\) is measured in metres, \(t\) in hours after midnight and \(30 t\) is in degrees.
[0pt] [The values 2 and 1.5 represent the relative effects of the moon and sun respectively.]

1. Show that \(2 \sin 30 t + 1.5 \cos 30 t\) can be written in the form \(2.5 \sin ( 30 t + \alpha )\), where \(\alpha\) is to be determined.
2. Find the height of tide at high water and the first time that this occurs after midnight.
3. Find the range of tide during the day.
4. Sketch the graph of \(h\) against \(t\) for \(0 \leq t \leq 12\), indicating the maximum and minimum points.
5. A sailing boat may enter the harbour only if there is at least 2 metres of water. Find the times during this morning when it may enter the harbour.
6. From your graph estimate the time at which the water falling fastest and the rate at which it is falling.