The depth (D metres) of water in a harbour at a time (t hours) after midnight on a particular day can be modelled by the functionwhere radians have been used.Select the two options which are correct statements about the predictions based on this model.Question 24Select one or more:At midday the depth is approximately 9 metres. The model can be used to predict the tide for up to 13 days. At midnight the depth is approximately 4.3 metres.The smallest depth is 6 metres. The time between the two high tides is exactly 12 hours. The largest depth is 9 metres.The depth of water in the harbour falls after midnight.

Identify the approximate time between high tide and the next low tide.6 hours12 hours18 hours24 hoursI'm not sure

Sarah studied this tide chart, written in 24-hour time, to choose when to go fishing at Batemans Bay.Sydney TidesNote: subtract 5 minutes for Batemans Bay tides.Day Low Tides High TidesTime Height Time HeightWed 0844 hrs 0.5 m 0152 hrs 1.7 m2041 hrs 0.6 m 1500 hrs 1.2 mThu 0940 hrs 0.5 m 0300 hrs 1.8 m2154 hrs 0.5 m 1601 hrs 1.3 mWhat was the shortest duration between high tides?A. 0152 hrsB. 1 h 8 minC. 12 hrsD. 1449 hrs

When the tide rises, the water level will also rise, causing the ladder to rise with it. Since the ladder is 200cm long and the distance between each rung is 20cm, there are a total of 10 rungs on the ladder.Initially, the bottom rung touches the water, so the water level is at 0cm. As the tide rises at a rate of 10cm per hour, the water level will reach the first rung after 1 hour, the second rung after 2 hours, and so on.To find out when the water will reach the fifth rung, we need to calculate how many hours it will take for the water level to rise to 80cm (4 rungs x 20cm each).Since the tide rises at a rate of 10cm per hour, it will take 8 hours (80cm / 10cm per hour) for the water to reach the fifth rung.

4. A small boat at a pier is planning to sail to a port end baek on a Sunday morning between 7am and 12pm. The journey takes 1.5 hours and must cross under a bridge.It takes exactly 0.5 hours to reach the spot under the bridge.The vertical distance from the surface of the water to the highest point of the boat’s mast is 5.6 metres(assumming this is constant at all times).The height of the bridge above the sea floor is 8.5 metres.To safely pass under the bridge,the gap between the top of the mast and the bridge must be at least 0.5m. In one particular week,the depth of the tide in the area can be modelled by the equation D(t)=1.1sin(0.51t-1)+1.88 where D is depth of the water in metres and t is time in hours after Sunday midnight.There is a restriction on the boat and that is, it can only sail when the depth of water is at least 1 m. Hint: Sketch the graph of D(t) first to get a 'feel’for the tidal change over times through the day and into the evening. You may also sketch the graph 1.1sin(0.51t-1)+1.88 +5.6 which shows the highest point of the boat above the sea floor at any time t. (a) What is the depth of the water at high tide? [2 marks] (b) What is the depth of the water at low tide? [2 marks] (c)How long is one low tide to the next? [2 marks] Hint: This would be the period. (d) What time is the first high tide and low tide? [4 marks] (e) Assumming that the boat does not stop once it starts sailing,between what times must the boat leave (no earlier than 7am and no later than 12pm)in order to get to the port safely?[7 marks]

A ship anchored in a port has a ladder which hangs over the side. The length of the ladder is 200cm, the distance between each rung in 20cm and the bottom rung touches the water. The tide rises at a rate of 10cm an hour. When will the water reach the fifth rung?