- The depth of water, \(D\) metres, in a harbour on a particular day is modelled by the formula
$$D = 5 + 2 \sin ( 30 t ) ^ { \circ } \quad 0 \leqslant t < 24$$
where \(t\) is the number of hours after midnight.
A boat enters the harbour at 6:30 am and it takes 2 hours to load its cargo. The boat requires the depth of water to be at least 3.8 metres before it can leave the harbour.
- Find the depth of the water in the harbour when the boat enters the harbour.
- Find, to the nearest minute, the earliest time the boat can leave the harbour. (Solutions based entirely on graphical or numerical methods are not acceptable.)