The given problem seems to be a part of a mathematics exam or assignment involving trigonometric functions and their applications. Here's a breakdown of the problem and what it's asking:

1. Part (e) asks for the latest time before 12:00 noon that Naomi can enter the harbour, given that the water depth must be at least 6 meters.

2. Part (f) requires calculating the length of time (in minutes) between 06:00 and 15:00 on 20 January during which Naomi cannot enter or leave the harbour.

Suggested Approach

1. Understand the Trigonometric Function: The problem likely uses a trigonometric function to model the depth of the water as a function of time. If provided, we should analyze that function to determine the times when the depth is at least 6 meters.

2. Find Time Intervals:

   • For part (e), identify the last time before 12:00 where the depth is 6 meters or more.
   • For part (f), calculate the total time interval where the depth is below 6 meters between 06:00 and 15:00.

Next Steps

If you have the trigonometric function or additional information about the depth of water, I can provide a detailed solution. Please provide that function or let me know if you'd like to continue with solving based on general assumptions.

Do you want to proceed with detailed calculations or share additional information?

Related Questions:

1. What type of trigonometric function is used to represent the depth of water (e.g., sine, cosine)?
2. Is the amplitude or period of the function provided?
3. Can you provide the equation of the depth function, if known?
4. Is there a graphical representation of the water depth available?
5. Are there constraints on the times or other information that would affect the solution?

Tip: In trigonometric applications, understanding the period and amplitude of the function is crucial for determining key time intervals accurately.