Question

The maximum height of water near a tidal power station in New Brunswick is 6.4 metres at 4:30 am and the minimum height is 3.6 m, 6.2 hours later. What is the depth of the water at 6:45 pm? a) 2.8 m b) 6.8 m c) 5.8 m d) 5.0 m

Answer 1

Part a)

Let the tide height be modelled by a cosine function

Let t=0 at 430am, h1= 6.4 m

Min height h2= 3.6 m at t=6.2 hrs.

Thus amplitude of cos function is A=(h1-h2)/2= 1.4

Mid line= 5

Time period T= 6.2*2= 12.4 hrs

W= 2π/T= 2π/12.4

Thus height = 1.4cos(πt/6.2)+5 metres

Height at 645pm, be H

t= 12+1+1+0.25= 14.25 hrs

H= 6.39 metres

Depth=6.39-3.6= 2.8m ....(answer)

Part b)

Time period of I revolution = 60 sec

h1=10

h2=2

K=2π/time period =2π/60= π/30 ...(answer)

Part c)

Time period of revolution T= 40sec

h2=5

h1=1

Thus diameter=h2-h1=4

Radius = d/2=2m ....(answer)