# Math Help - Periodic Function

1. ## 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

2. 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.