Math - the Low and High Tides’ Height

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C→ if , D at 0000(12am)[pic 26]

However, in this case, D is at 1100

[pic 27]

Since the point after D is min, it is an inverse Sin graph

, where t = time in 24hrs after the midnight on 19th of September.[pic 28]

Sunrise time=0600 sunset time=1803

To find the time period when the floor of the river/sea could be seen through the glass-bottomed boat, the visibility through the water on the 19th of September (in meter) should be greater or at least equal to the water depth.

It is obvious that the visibility of the water is greater than the height of the tides during the time period between 0154 to 0742, and 1636 to 1742. This means that the water is clear enough to be seen through.

Assume that the water only can be seen through during daytime that is after sunrise (0600) and before sunset (1803). Therefore, the time period that the water could be seen through is from 0600 to 0712 and 1636 to 1742.

[pic 29][pic 30][pic 31][pic 32]

[pic 33]

The result determined using the hand drawn graph was not very precise because the points are roughly plotted on the graph. This graph however, is accurately graphed on a graphic calculator. From the graph above, it is evident that the water can be seen through during the time period from 0600 (line x=6) to 0759 (7.974) and 1644 (16.733) to 1742 (17.691). Same as the graph above, the hand drawn graph has 4 interceptions at similar spot. The result obtained from this graph is quite close to the result from the hand drawn graph, where the differences between the second interception of the two graph is 17 minutes; the third interceptions is 8 minutes; and finally the last interceptions are at the same time. Hence, the result from the hand drawn graph is considered reasonableness.