A water wave traveling in a straight line on a lake is described by the equation

Question

A water wave traveling in a straight line on a lake is described by the equation

y(x,t) = (3.75cm)cos(0.450cm-1x + 5.40s-1t) where y is the displacement perpendicular to the undisturbed surface of the lake. What is the maximum speed of his cork floater as the wave causes it to bob up and down? There is a solution of this question on cramster but the answer is not right. I calculated period (T) to be 1.16 seconds and then tried to calculate the maximum velocity by dividing 3.75 by 1.16, but I don't get the right answer. Can someone please help?
y(x,t) = (3.75cm)cos(0.450cm-1x + 5.40s-1t) where y is the displacement perpendicular to the undisturbed surface of the lake. What is the maximum speed of his cork floater as the wave causes it to bob up and down? There is a solution of this question on cramster but the answer is not right. I calculated period (T) to be 1.16 seconds and then tried to calculate the maximum velocity by dividing 3.75 by 1.16, but I don't get the right answer. Can someone please help?
What is the maximum speed of his cork floater as the wave causes it to bob up and down? There is a solution of this question on cramster but the answer is not right. I calculated period (T) to be 1.16 seconds and then tried to calculate the maximum velocity by dividing 3.75 by 1.16, but I don't get the right answer. Can someone please help?

Explanation / Answer

A water wave traveling in a straight line on a lake is described by the equation


y(x,t) = (3.75cm)cos(0.450cm-1x + 5.40s-1t)
Now speed of wave is          v = dy/dt             = (d/dt)[(3.75cm)cos(0.450cm-1x + 5.40s-1t)]             = -(3.75cm)(5.40s-1)sin(0.450cm-1x + 5.40s-1t) Therefore max speed = (3.75cm)(5.40s-1)                                    = 20.25 cm/s

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