Tides the table at the right shows the times for high tide and low tide of one day. The markings on the side of the local pier showed a high tide of 7ft and a low tide of 4ft on the previous day.
tide chart
High Tide 4:03am
Low Tide 10:14am
High Tide 4:25pm
Low Tide 10:36pm
a.What is the average depth of water at the pier?What is the amplitude of the variation from the average depth?
-use the cosine function:y=acosbt
The amplitude is |a|=1/2 (maximum height-minimum height)
=1/2 (7-4)=1.5 & since we start with high tide
then a >0 so a=1.5ft
Average depth =((maximum high tide+minimum low tide))/2=(7+4)/2=11/2=5.5 ft
b.How long is one cycle of the tide?
I found my a part but i dont know how to find b? equation use for part b is period =2π/B
3 answers
you know that the distance between a max and a min for the cosine function is 1/2 period. The table shows some variation in that, but it is clear that there are two high and two low tides each day. So the period will be about 12 hours, right?
More like 12.5 hours, about an hour later every day. (In Gloucester at least :)
the answer is 12hr 22min or B= 60pi/371 i dont understand how they got the answer to part b
1 answer