Question

A buoy in the harbor of san juan,puerto rico, bobs up and down.The distance between the highest and lowest point is 3 feet.It moves from its highest point down to its lowest point and back to its highest point every 8 seconds.
a)Find the equation of the motion for the buoy assuming that it is at its equilibrium point at t=0 and the buoy is on its way down at that time.
b)Determine the height of the buoy at 3 seconds.
c)Determine the height of the buoy at 12 seconds.

Answer 1

you can use
\[1.5\sin(bx)\] which will give you the correct amplitude. the period is 8 so solve
\[\frac{2\pi}{b}=8\] to get
\[b=\frac{\pi}{4}\] and your function is
\[1.5\sin(\frac{\pi}{4}x)\]

Answer 2

oh that is wrong, because it is on its way down. sorry
use
\[-1.5\sin(\frac{\pi}{4}x)\]

Answer 3

good, ty It match with my answer