Posted by **Farah** on Saturday, November 27, 2010 at 12:01pm.

An oceanographer measured a set of sea waves during a storm and modelled the vertical displacement of waves in meters using the equation h(t)=0.6cos2t+0.8sint, where t is the time in seconds.

a) Determine the vertical displacement of the wave when the velocity is 0.8m/s

Ans: -1.2sin2t+0.8cost = 0.8

-2.4(sint)(cost)+0.8cost = 0.8

cost(-2.4sint+0.8) = 0.8

cost = 0.8

t = cos-1(0.8) OR -2.4sint +0.8 = 0.8

=0.6 t = 0

b) Determine the maximum velocity of the wave and when it occurs.

Ans: cost(-2.4sint+0.8)=0

therefore t= 1.5 and 0.3 and Vmax occurs at t=1.5s

c) When does the wave first change from a hill to a trough? Explain.

Please check the above answers and help if they are incorrect, and need guidance with part c, is it asking for the height?

- Math - app of sinusoial derivatives (help+check) -
**drwls**, Saturday, November 27, 2010 at 1:37pm
a) is correct for a while, but you cannot go from

cost(-2.4sint+0.8) = 0.8

to an assumption that one or the other factor is 0.8. That only works if the product is zero, in which case either factor must be zero.

Rewrite as

cost(-3sint +1) = 1

One solution to that is t = 0.

Another (obtained numerically) is about at 4.97 radians.

For (c), look for the value of t where h(t) = 0. It will be changing from a hill to a trough there. You can rewite the h(t) equation as a quadratic in sin t.

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