Question 773627: Hello, I've had trouble solving this word problem..."At the ocean it is known that the tide follows a trigonometric path. At high tide, the water comes in to a point 1 meter from where I placed the flag. At low tide, the water comes in to a point 11 meters from the same flag. The time it takes from to get from high tide to low tide is 5 hours. It is now midnight and it is high tide.
a) State a possible equation for this motion.
b) We want to wake up and go to the beach when we can set up our towels at a time between 10 a.m. and 2 p.m. the next day when the water will be 4 meters from our flag. At what time will this be?"
I've figured out that the low tide is the maximum and the high tide is the minimum but I don't know how to proceed...Help?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! ..."At the ocean it is known that the tide follows a trigonometric path. At high tide, the water comes in to a point 1 meter from where I placed the flag. At low tide, the water comes in to a point 11 meters from the same flag. The time it takes from to get from high tide to low tide is 5 hours. It is now midnight and it is high tide.
a) State a possible equation for this motion.
The period is 10 hours.
The amplitude is 10 meters
h(t) = 10sin(2pi*t/10)
h(t) = 10sin(pi*t/5), t in hours, h in meters
Measured from the flag, it's
h(t) = 10sin(pi*t/5) + 1
That gives a sinusoidal motion from 1 m to 11 m from the flag, with t = 0 at midnight.
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b) We want to wake up and go to the beach when we can set up our towels at a time between 10 a.m. and 2 p.m. the next day when the water will be 4 meters from our flag. At what time will this be?
h(t) = 10sin(pi*t/5) + 1 = 4
10sin(pi*t/5) = 3
sin(pi*t/5) = 0.3
pi*t/5 =~ 0.305
t = 0.305*5/pi hours after midnight
t =~ 0.484 hours > midnight = 0029
t = pi - 0.484 = 2.657 hours > midnight = 0239, still too early
The period is 10 hours, so it's at 4 meters again at 1029 & 1239
Its distance from the flag increases from 4 meters at 1029 as the tide goes out, then is at 4 meters from the flag at 1239 as the tide comes in.
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PS The water level is highest at high tide, lowest at low tide (measured from the bottom).
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