A tidal wave reaches low tide at 3:00AM and high tide at 3:00PM.

Question

The tide can rise and fall 10m from the sea level.
If at low tide the water level is 2m above the seabed (bottom of the sea)
a) determine an equation to model the sea level above the sea bed S and time t in hours after midnight

b). Sketch the graph for the tidal wave over a 48 hour window

Really need help with this guys :(

Answer 1

low tide at 3:00AM and high tide at 3:00PM
so, the period is 24 hours. Since sin(kt) has period 2π/k, we start out with

y = sin(π/12 t)

rise-fall = 10, so

y = 10sin(π/12 t)

low tide is at +2, so

y = 12+10sin(π/12 t)

We are starting out near the minimum value for t=0. cos(t) has a maximum at t=0, but we want a minimum at t=3. So, let's make that

y = 12-10cos(π/12 (t-3))

And the graph is at

http://www.wolframalpha.com/input/?i=12-10cos(%CF%80%2F12+(t-3))+for+t%3D0..24

By the way, you do know that the tide has a period of roughly 12 hours, not 24, right?