4. On a particular day, high tide at the entrance to a harbour occurs at 11 a.m. and the water depth is 14 m . Low tide occurs \(6 \frac { 1 } { 4 }\) hours later at which time the water depth is 6 m . In a model of the situation, the water level is assumed to perform simple harmonic motion.
Using this model,

1. write down the amplitude and period of the motion. A ship needs a depth of 9 m before it can enter or leave the harbour.
2. Show that on this day a ship must enter the harbour by 2.38 p.m., correct to the nearest minute, or wait for low tide to pass.
   (6 marks)
   Given that a ship is not ready to enter the harbour until 5 p.m.,
3. find, to the nearest minute, how long the ship must wait before it can enter the harbour.