Answer:
Step-by-step explanation:
Given
[tex]Y=15+\sin (2\pi t)[/tex]
(a)Vertical velocity v at time t
[tex]\frac{\mathrm{d} y}{\mathrm{d} t}=0+2\pi \cos (2\pi t)[/tex]
[tex]v_y=2\pi \cos (2\pi t)[/tex]
graph of y is similar to sin x but is it shifted by a unit of 15 units and repeat itself after 1 s
Graph of v(t) is similar to cos x but it is amplified by a factor of [tex]2\pi [/tex]
a. The vertical velocity, v, of the boat at time t is v = 2cos(2πt)
b. Find graphs of y and v against t in the attachment below
Since the boat at anchor is bobbing up and down in the sea. The vertical distance, y, in feet, between the sea floor and the boat is given as a function of time, t, in minutes, by y = 15 + sin(2πt).
The vertical velocity of the boat is the time derivative of the vertical distance, y.
So, y = 15 + sin(2πt).
v = dy/dt
v = d[15 + sin(2πt)]/dt
v = d[15]/dt + d[sin(2πt)]/dt
v = 0 + 2cos(2πt)
v = 2cos(2πt)
So, the vertical velocity, v, of the boat at time t is v = 2cos(2πt)
Find graphs of y and v against t in the attachment below
Learn more about sine graphs here:
https://brainly.com/question/26497319
