Maths B!!!

Question

1. The depth of water, d(t) m, at a pier changes according to the rule

                                     d(t)=5+2 cos(pi/6)t

where t is the time in hours from high tide. On March 18, high tide occurred at 7:30am

 

a) Draw a sketch showing the depth of water for the 24 hours after 7:30am on 18 March

Answer 1

First evaluate cos(\pi/6) = \sqrt(3)/2=M

thus d(t)=5+2Mt

 

This is the equation for a line with slope 2M and y-intercept 5.

 

I am not sure this actually models ebbs and flows of tides...

 

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Did you copy the problem correctly?  Should d(t) = 5+2cos(\pi/6 * t)

 

If t is inside the parenthesis, you would need to graph a sine curve that has been translated in the plane appropriately...This would model the cyclical nature of tides more closely...although the periodicity would be off from what is expected.

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High tide would occur at the maximal point for depth, which should be at t=0 if the t was inside the argument of the cosine function...This leads me to believe the problem is probably what I put above, between the ****'s.

 

Hope this helps!