Math  app of sinusoial derivatives (help+check)
posted by Farah .
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 = cos1(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?

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. 
The first two answers are wrong because when you have an equation that is 1= (x)(y) you cannot split it into 1=x and 1=y. Simply because when you do that although you find when x=1 when x=1 that doesn't mean y=1. The second answer is wrong because they are looking for maximum velocity which is found by taking the second derivative and setting it equal to 0 and subbing that back into the first derivative.
Respond to this Question
Similar Questions

Math pplication of Sin and Cos&thier derivative
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 … 
Math  app of Sine and Cosine & thier Derivatives
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 … 
physics
while watching ocean waves at the dock of the bay. otis notices that 10 waves pass beneath him in 30 seconds. he also notices that the crests of succesive waves exactly coincide with the posts that are 5 meters apart. what are the … 
Physics
While watching ocean waves at the dock of the bay, Otis notices that 10 waves pass beneath him in 30 seconds. He also notices that the crests of successive waves exactly coincide with the posts that are 5 meters apart. What are the … 
physics
An earthquake generates three kinds of waves: surface waves (L waves), which are the slowest and weakest; shear (S) waves, which are transverse waves and carry most of the energy; and pressure (P) waves, which are longitudinal waves … 
physics
An earthquake generates three kinds of waves: surface waves (L waves), which are the slowest and weakest; shear (S) waves, which are transverse waves and carry most of the energy; and pressure (P) waves, which are longitudinal waves … 
Algebra 1 high school
In deep water, the speed s (in meters per second) of a series of waves and the wavelength L (in meters) of the waves are related by the equation 2(pi)s^2=9.8L. a. Find the speed the the nearest hundredth of a meter per second of a … 
Physics
The velocity of the transverse waves produced by an earthquake is 6.13 km/s, while that of the longitudinal waves is 9.9919km/s. A seismograph records the arrival of the transverse waves 61.5 seconds after that of the longitudinal … 
PreCalculus
During a storm a ship is being tossed up and down by huge waves. The vertical motion of the ship is given by the equation: h = 21cos((2π/5)t) where h is height above sea level in feet at time t minutes. 1) Give the first 2 times … 
scienice
a weatherman reports, "the storm waves are about 2 meters high and about 35 meters apart." what properties of waves is the reporter describing