Apply trigonometric methods in solving problems

[Guest]

Hey I was wondering if anyone could help me with this I'm stumped

Tides vary so the high tide and low tide height of the water is different every day. At certain times of the year, such as a Spring tide, the water can be very deep and it may not be safe to cross the inlet. During one big tide, the water was 3.9 metres deep at high tide and 0.7 metres deep at low tide.
The Department of Conservation (DOC) recommends that walkers only cross the inlet within one and a half hours before low tide and two hours after low tide.
Find a safe time to cross the inlet during this big tide and discuss DOC’s recommendation in relation to your findings for both tidal situations.

[Guest]

To find a safe time to cross the inlet during the big tide, we need to consider the difference between high tide and low tide, which is 3.9 - 0.7 = 3.2 meters.

According to DOC's recommendation, walkers should only cross the inlet within one and a half hours before low tide and two hours after low tide. This means we need to find a time frame when the tide is close to low tide but still rising.

Let's denote the time of low tide as T, and the time before low tide as T - 1.5 hours, and the time after low tide as T + 2 hours.

If we consider the high tide depth (3.9 meters) and subtract the difference between high tide and low tide (3.2 meters), we get a depth of 0.7 meters, which is the same as the depth at low tide. Therefore, the safe time to cross the inlet during the big tide would be at high tide.

Now, let's discuss DOC's recommendation in relation to these findings for both tidal situations:

Big Tide (3.9 meters at high tide, 0.7 meters at low tide):

According to DOC, walkers should only cross within one and a half hours before low tide and two hours after low tide. However, during a big tide, the water depth at low tide is only 0.7 meters, which might not provide enough depth for safe crossing. Therefore, it would be safer to cross closer to high tide, when the depth is 3.9 meters.

Normal Tide (varying depth between high and low tide):

During a normal tide, where the depth varies between high and low tide, DOC's recommendation makes sense. Crossing within one and a half hours before low tide and two hours after low tide ensures that walkers cross when the water depth is manageable and not excessively deep or shallow.

In summary, while DOC's recommendation is generally suitable for normal tidal situations, during a big tide it's safer to cross closer to high tide when the water depth is deeper and more suitable for crossing.

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