A vessel is crossing a channel. The depth of the water(measured in metres) varies with time and is represented by the following equation:

Question

d(t)=2.5sin(0.523t)+2.9
a. create a graph showing the depth of the water over 24 hours.
b. what is the period of this function and what does it represent about the varying depths of the water.
c. the vessel requires a depth of at least 1.3m of water to cross the channel. They want to make 2 trips/day with each trip lasting at least 5 hours. What times could these trips be scheduled to allow for safe navigation?

Answer 1

(a) see

http://www.wolframalpha.com/input/?i=plot+2.5sin%280.523t%29%2B2.9+for+t%3D0+to+24

(b) since sin(kt) has period 2π/k,
sin(.523t) has period 2π/.523 = 12.01

That is, the tide cycles every 12 hours.

(c) look at the graph and see where d(t) >= 1.3

You want intervals at least 5 hours long

Answer 2

Is there somewhere a person can see the answer?