[MOVED] Trig Functions: modelling tidal water depth

[sweetliljenny]

In a tidal river, the time between high tide and low tide is 6.2 hours. At high tide, the depth of he water is 17.2 feet, while at low tide, the depth is 5.6 feet. Assume the water depth is a trigonometic function of time.

a) Graph the depth of the water over time if there is a high tide at 12:00 noon. Label your graph, indicating the high and low tide.

b) Write an equation for the curve you drew in part (a).

c) A boat requires a depth of 8 feet to sail, and is docked at 12:00 noon. What is the latest time in the afternoon it can set sai? Your answer should be accurate to the nearest minute.

So far, I have gotten that the amplitude is 5.8 and that the midline is 11.4.

 

[wjm11]

in a tidal river, the time between high tide and low tide is 6.2 hours. At high tide the depth of he water is 17.2 feet, while at low tide the depth is 5.6 feet. Assume the water depth is a trigonometic function of time.

a) Graph the depth of the water over time if there is a high tide at 12:00 noon. Label your graph, indicating the high and low tide.

b) Write an equation for the curve you drew in part (a).

c) A boat requires a depth of 8 feet to sail, and is docked at 12:00 noon. What is the latest time in the afternoon it can set sai? Your answer should be accurate to the nearest minute.


so far i got that the amp is 5.8
and that the midline is 11.4

Hi, Jenny,

First, draw yourself a sketch of the graph. You have two known points: (12 noon, 17.2) and (12 noon + 6.2 hrs, 5.6). Draw dotted, horizontal lines through these two points; they are the upper and lower bounds of your curve, as they are at high and low tides. Draw a third dotted, horizontal line through the midpoint, which you correctly identified as 11.4, the average of high and low tides.

What is the period of this function? If it’s 6.2 hrs between high and low, that’s one half of the period, so the period is 12.4 hrs. Therefore, you can put a third point on your graph: (12 noon + 12.4 hrs, 17.2).

Can you continue from here?