The depth of water at the end of a pier varies with the tides throughout the day. Today the high tide occurs at 4:15 am with a depth of 5.2 m. The low tide occurs at 10:27 am with a depth of 2.0 m.

Question

a) 4:15 = ? hrs and 10:27 = ? hrs after midnight.

b) When would the next high tide and low tide occur (give both the clock time and hrs. after midnight)?

c) Graph the information from the given situation using your part (a) and (b) information to include 2 high tides and 2 low tides. Connect with a smooth curve. Use a graph similar to the one below. (do not use the one below – too small!)

d) Calculate the values of the Amplitude, Axis of the wave and Period.

e) From the information in (d) and the appropriate Phase Shift, write a cosine equation that models the depth of the water

I don't need help with c but I am most confused with parts a and b.

Answer 1

4:15 AM is 4hrs and 15 minutes after midnight

10:27AM is 10hrs and 27 minutes after midnight

It takes 6hrs and 12 minutes to go from high tide to low tide. It will,take another 6hrs and 12 minutes to return to high tide which would be at 10:27 AM plus 6 hrs and 12 minutes which would be at 4:39PM or 16hrs and 39 minutes past midnight

The next low tide will be 6 hrs and 12 minutes later or 10:51PM or 22hrs and 51 minutes past midnight

As far as the equation goes the midline or vertical shift is (5.2 +2.0)/2 or 3.6 and the amplitude is 5.2-3.6=1.6

phase shift is 4.25 hours to the right and the period is 12hrs and 24 minutes Need to have both these in the same units so will use hours. 12 hrs and 24 minutes is 12.4 hours

Now can calculate B for the cosine equation B= (2pi)/12.4= pi/6.2

y= 1.6cosine [pi/6.2(x-4.25)] +3.6