# Periodic Function

• Oct 29th 2006, 02:21 AM
needmathshelp
Periodic Function
Hey can anyone help me with this Q

Mr Johnston is a very keen fisherman who will go fishing at any time of the day or night. He requires 1.5 metres of water at the boat ramp (ie. 1.5 m above the mean sea level) to launch his boat the "Periodic Function". The next high tide occurs at 2am, at a height of 2.8m above the mean sea level

a) Find the times in teh first 24 hours after 2am when he is able to launch his boat

thanx heaps
• Oct 29th 2006, 06:36 AM
earboth
Quote:

Originally Posted by needmathshelp
Hey can anyone help me with this Q

Mr Johnston is a very keen fisherman who will go fishing at any time of the day or night. He requires 1.5 metres of water at the boat ramp (ie. 1.5 m above the mean sea level) to launch his boat the "Periodic Function". The next high tide occurs at 2am, at a height of 2.8m above the mean sea level

a) Find the times in teh first 24 hours after 2am when he is able to launch his boat

thanx heaps

Hi,

I assume that the height of the water level can be described approximately by a cos-function. (In real life this assumption is not true)

In 24 hours you have 2 high tides and 2 low tides. If one high tide is at 2 am, then there is another at 4 pm and the next at 2 am, and so on...

The maximum height is 2.8 m at 2 am. Screw all these parts together and you'll get the depth of water as a function with respect to time t:

$d(t)=2.8 \cdot \cos\left(\frac{\pi}{6} \left(t-2 \right) \right)$

Now you know that d(t) >= 1.5. That means you have to solve the equation for t:

$1.5 \leq 2.8 \cdot \cos\left(\frac{\pi}{6} \left(t-2 \right) \right)$

I got: 2 am < t < 3.92 am or 0.08 pm < t < 3.92 am or 0.08 am < t < 2 am

EB

I've attached an image to sho you the graph of the function.