A 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). (a) Find the vertical velocity, v, of the boat at time t. (b) Make rough sketches of y and v against t.

Accepted Solution

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 sGraph of v(t) is similar to cos x but it is amplified by a factor of [tex]2\pi [/tex]