2025 CHS PRELIMS P2 Q5

The depth of water, \(h\) metres, in a shallow port on a particular day is modelled by the formula

\[h=7+2\sin\left(\frac{\pi}{6}t\right),\]

where \(t\) is the number of hours after midnight.

1. State the period of \(h\).[1]
2. Use the model to predict the time when the depth of water is at its lowest.[2]

A supply boat docks at the port at 5.30 am and it takes the workers 3 hours to unload its cargo immediately after it docks. To leave the port safely, the supply boat requires the depth of water to be at least 5.6 metres.

4. Determine the earliest time, to the nearest minute, that the supply boat can leave the port.[4]