February 25, 2017

Homework Help: Math - app of sinusoial derivatives (help+check)

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?

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